mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -1132,7 +1132,7 @@ theorem uniformIntegrable_average_real (hp : 1 ≤ p) {f : ℕ → α → ℝ} (
       · rw [Set.indicator_const_smul s (↑n)⁻¹ (f i)]
         rfl
       · rfl
-    simp_rw [this, snorm_const_smul, ← Finset.mul_sum, nnnorm_inv, Real.nnnorm_coe_nat]
+    simp_rw [this, snorm_const_smul, ← Finset.mul_sum, nnnorm_inv, Real.nnnorm_natCast]
     by_cases hn : (↑(↑n : ℝ≥0)⁻¹ : ℝ≥0∞) = 0
     · simp only [hn, MulZeroClass.zero_mul, zero_le]
     refine' le_trans _ (_ : ↑(↑n : ℝ≥0)⁻¹ * n • ENNReal.ofReal ε ≤ ENNReal.ofReal ε)
@@ -1140,8 +1140,8 @@ theorem uniformIntegrable_average_real (hp : 1 ≤ p) {f : ℕ → α → ℝ} (
       conv_rhs => rw [← Finset.card_range n]
       exact Finset.sum_le_card_nsmul _ _ _ fun i hi => hδ₂ _ _ hs hle
     · simp only [ENNReal.coe_eq_zero, inv_eq_zero, Nat.cast_eq_zero] at hn
-      rw [nsmul_eq_mul, ← mul_assoc, ENNReal.coe_inv, ENNReal.coe_nat,
-        ENNReal.inv_mul_cancel _ (ENNReal.nat_ne_top _), one_mul]
+      rw [nsmul_eq_mul, ← mul_assoc, ENNReal.coe_inv, ENNReal.coe_natCast,
+        ENNReal.inv_mul_cancel _ (ENNReal.natCast_ne_top _), one_mul]
       · exact le_rfl
       all_goals simpa only [Ne.def, Nat.cast_eq_zero]
   · obtain ⟨C, hC⟩ := hf₃
@@ -1152,7 +1152,7 @@ theorem uniformIntegrable_average_real (hp : 1 ≤ p) {f : ℕ → α → ℝ} (
       intro i
       ext ω
       simp only [mul_comm, Pi.smul_apply, Algebra.id.smul_eq_mul]
-    simp_rw [this, snorm_const_smul, ← Finset.mul_sum, nnnorm_inv, Real.nnnorm_coe_nat]
+    simp_rw [this, snorm_const_smul, ← Finset.mul_sum, nnnorm_inv, Real.nnnorm_natCast]
     by_cases hn : (↑(↑n : ℝ≥0)⁻¹ : ℝ≥0∞) = 0
     · simp only [hn, MulZeroClass.zero_mul, zero_le]
     refine' le_trans _ (_ : ↑(↑n : ℝ≥0)⁻¹ * (n • C : ℝ≥0∞) ≤ C)
@@ -1160,8 +1160,8 @@ theorem uniformIntegrable_average_real (hp : 1 ≤ p) {f : ℕ → α → ℝ} (
       conv_rhs => rw [← Finset.card_range n]
       exact Finset.sum_le_card_nsmul _ _ _ fun i hi => hC i
     · simp only [ENNReal.coe_eq_zero, inv_eq_zero, Nat.cast_eq_zero] at hn
-      rw [nsmul_eq_mul, ← mul_assoc, ENNReal.coe_inv, ENNReal.coe_nat,
-        ENNReal.inv_mul_cancel _ (ENNReal.nat_ne_top _), one_mul]
+      rw [nsmul_eq_mul, ← mul_assoc, ENNReal.coe_inv, ENNReal.coe_natCast,
+        ENNReal.inv_mul_cancel _ (ENNReal.natCast_ne_top _), one_mul]
       · exact le_rfl
       all_goals simpa only [Ne.def, Nat.cast_eq_zero]
 #align measure_theory.uniform_integrable_average MeasureTheory.uniformIntegrable_average_real

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -359,7 +359,7 @@ theorem Memℒp.snorm_indicator_norm_ge_pos_le (hf : Memℒp f p μ) (hmeas : St
 
 end
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], [], []]: ./././Mathport/Syntax/Translate/Basic.lean:354:22: unsupported: parse error @ arg 0: next failed, no more args -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], [], []]: ./././Mathport/Syntax/Translate/Basic.lean:355:22: unsupported: parse error @ arg 0: next failed, no more args -/
 #print MeasureTheory.snorm_indicator_le_of_bound /-
 theorem snorm_indicator_le_of_bound {f : α → β} (hp_top : p ≠ ∞) {ε : ℝ} (hε : 0 < ε) {M : ℝ}
     (hf : ∀ x, ‖f x‖ < M) :
@@ -382,7 +382,7 @@ theorem snorm_indicator_le_of_bound {f : α → β} (hp_top : p ≠ ∞) {ε : 
   have haebdd : ∀ᵐ x ∂μ.restrict s, ‖f x‖ ≤ M :=
     by
     trace
-      "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], [], []]: ./././Mathport/Syntax/Translate/Basic.lean:354:22: unsupported: parse error @ arg 0: next failed, no more args"
+      "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], [], []]: ./././Mathport/Syntax/Translate/Basic.lean:355:22: unsupported: parse error @ arg 0: next failed, no more args"
     exact fun x => (hf x).le
   refine' le_trans (snorm_le_of_ae_bound haebdd) _
   rw [measure.restrict_apply MeasurableSet.univ, univ_inter, ←
@@ -828,7 +828,7 @@ theorem unifIntegrable_of' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → 
       by
       refine' add_le_add_left _ _
       rw [← ENNReal.ofReal_coe_nnreal, ← ENNReal.ofReal_mul (NNReal.coe_nonneg _), ← div_div,
-        mul_div_cancel' _ (NNReal.coe_pos.2 hCpos).Ne.symm]
+        mul_div_cancel₀ _ (NNReal.coe_pos.2 hCpos).Ne.symm]
       exact le_rfl
     _ ≤ ENNReal.ofReal ε :=
       by

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -190,7 +190,7 @@ theorem tendsto_indicator_ge (f : α → β) (x : α) :
   refine' lt_of_le_of_lt (Nat.le_ceil _) _
   refine' lt_of_lt_of_le (lt_add_one _) _
   norm_cast
-  rwa [ge_iff_le, coe_nnnorm] at hn 
+  rwa [ge_iff_le, coe_nnnorm] at hn
 #align measure_theory.tendsto_indicator_ge MeasureTheory.tendsto_indicator_ge
 -/
 
@@ -218,13 +218,13 @@ theorem Memℒp.integral_indicator_norm_ge_le (hf : Memℒp f 1 μ) (hmeas : Str
         hmeas.nnnorm.measurable.coe_nnreal_real.strongly_measurable
   have hbound : has_finite_integral (fun x => ‖f x‖) μ :=
     by
-    rw [mem_ℒp_one_iff_integrable] at hf 
+    rw [mem_ℒp_one_iff_integrable] at hf
     exact hf.norm.2
   have := tendsto_lintegral_norm_of_dominated_convergence hmeas hbound _ htendsto
-  · rw [ENNReal.tendsto_atTop_zero] at this 
+  · rw [ENNReal.tendsto_atTop_zero] at this
     obtain ⟨M, hM⟩ := this (ENNReal.ofReal ε) (ENNReal.ofReal_pos.2 hε)
     simp only [true_and_iff, ge_iff_le, zero_tsub, zero_le, sub_zero, zero_add, coe_nnnorm,
-      mem_Icc] at hM 
+      mem_Icc] at hM
     refine' ⟨M, _⟩
     convert hM M le_rfl
     ext1 x
@@ -289,7 +289,7 @@ theorem Memℒp.snormEssSup_indicator_norm_ge_eq_zero (hf : Memℒp f ∞ μ)
     rw [← nonpos_iff_eq_zero]
     refine' (measure_mono this).trans _
     have hle := coe_nnnorm_ae_le_snorm_ess_sup f μ
-    simp_rw [ae_iff, not_le] at hle 
+    simp_rw [ae_iff, not_le] at hle
     exact nonpos_iff_eq_zero.2 hle
   rw [this, snorm_ess_sup_measure_zero]
   exact measurableSet_le measurable_const hmeas.nnnorm.measurable.subtype_coe
@@ -351,7 +351,7 @@ theorem Memℒp.snorm_indicator_norm_ge_pos_le (hf : Memℒp f p μ) (hmeas : St
     ⟨max M 1, lt_of_lt_of_le zero_lt_one (le_max_right _ _), le_trans (snorm_mono fun x => _) hM⟩
   rw [norm_indicator_eq_indicator_norm, norm_indicator_eq_indicator_norm]
   refine' indicator_le_indicator_of_subset (fun x hx => _) (fun x => norm_nonneg _) x
-  change max _ _ ≤ _ at hx 
+  change max _ _ ≤ _ at hx
   -- removing the `change` breaks the proof!
   exact (max_le_iff.1 hx).1
 #align measure_theory.mem_ℒp.snorm_indicator_norm_ge_pos_le MeasureTheory.Memℒp.snorm_indicator_norm_ge_pos_le
@@ -374,7 +374,7 @@ theorem snorm_indicator_le_of_bound {f : α → β} (hp_top : p ≠ ∞) {ε : 
     · ext x
       rw [Pi.zero_apply, ← norm_le_zero_iff]
       exact (lt_of_lt_of_le (hf x) hM).le
-  rw [not_le] at hM 
+  rw [not_le] at hM
   refine' ⟨(ε / M) ^ p.to_real, Real.rpow_pos_of_pos (div_pos hε hM) _, fun s hs hμ => _⟩
   by_cases hp : p = 0
   · simp [hp]
@@ -522,8 +522,8 @@ theorem unifIntegrable_fin (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) {n : ℕ} {f
   · rw [(_ : i = n)]
     · exact hδ₂ _ hs (le_trans hμs <| ENNReal.ofReal_le_ofReal <| min_le_right _ _)
     · have hi' := Fin.is_lt i
-      rw [Nat.lt_succ_iff] at hi' 
-      rw [not_lt] at hi 
+      rw [Nat.lt_succ_iff] at hi'
+      rw [not_lt] at hi
       simp [← le_antisymm hi' hi]
 #align measure_theory.unif_integrable_fin MeasureTheory.unifIntegrable_fin
 -/
@@ -540,7 +540,7 @@ theorem unifIntegrable_finite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞
   obtain ⟨δ, hδpos, hδ⟩ := unif_integrable_fin μ hp_one hp_top hg hε
   refine' ⟨δ, hδpos, fun i s hs hμs => _⟩
   specialize hδ (hn.some i) s hs hμs
-  simp_rw [hgeq, Function.comp_apply, Equiv.symm_apply_apply] at hδ 
+  simp_rw [hgeq, Function.comp_apply, Equiv.symm_apply_apply] at hδ
   assumption
 #align measure_theory.unif_integrable_finite MeasureTheory.unifIntegrable_finite
 -/
@@ -580,7 +580,7 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp
   rw [ENNReal.tendsto_atTop_zero]
   intro ε hε
   by_cases ε < ∞; swap
-  · rw [not_lt, top_le_iff] at h 
+  · rw [not_lt, top_le_iff] at h
     exact ⟨0, fun n hn => by simp [h]⟩
   by_cases hμ : μ = 0
   · exact ⟨0, fun n hn => by simp [hμ]⟩
@@ -595,7 +595,7 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp
   obtain ⟨δ₁, hδ₁, hsnorm₁⟩ := hui hε'
   obtain ⟨δ₂, hδ₂, hsnorm₂⟩ := hg'.snorm_indicator_le μ hp hp' hε'
   obtain ⟨t, htm, ht₁, ht₂⟩ := tendsto_uniformly_on_of_ae_tendsto' hf hg hfg (lt_min hδ₁ hδ₂)
-  rw [Metric.tendstoUniformlyOn_iff] at ht₂ 
+  rw [Metric.tendstoUniformlyOn_iff] at ht₂
   specialize
     ht₂ (ε.to_real / (3 * measure_univ_nnreal μ ^ (1 / p.to_real)))
       (div_pos (ENNReal.toReal_pos (gt_iff_lt.1 hε).Ne.symm h.ne) (mul_pos (by norm_num) hpow))
@@ -650,7 +650,7 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp
     by
     rw [ENNReal.ofReal_div_of_pos (show (0 : ℝ) < 3 by norm_num), ENNReal.ofReal_toReal h.ne]
     simp
-  rw [this] at hnf hng hlt 
+  rw [this] at hnf hng hlt
   rw [snorm_neg, ← ENNReal.add_thirds ε, ← sub_eq_add_neg]
   exact add_le_add_three hnf hng hlt
 #align measure_theory.tendsto_Lp_of_tendsto_ae_of_meas MeasureTheory.tendsto_Lp_of_tendsto_ae_of_meas
@@ -689,7 +689,7 @@ theorem unifIntegrable_of_tendsto_Lp_zero (hp : 1 ≤ p) (hp' : p ≠ ∞) (hf :
     (hf_tendsto : Tendsto (fun n => snorm (f n) p μ) atTop (𝓝 0)) : UnifIntegrable f p μ :=
   by
   intro ε hε
-  rw [ENNReal.tendsto_atTop_zero] at hf_tendsto 
+  rw [ENNReal.tendsto_atTop_zero] at hf_tendsto
   obtain ⟨N, hN⟩ := hf_tendsto (ENNReal.ofReal ε) (by simpa)
   set F : Fin N → α → β := fun n => f n
   have hF : ∀ n, mem_ℒp (F n) p μ := fun n => hf n
@@ -764,7 +764,7 @@ theorem unifIntegrable_of' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → 
   by
   have hpzero := (lt_of_lt_of_le zero_lt_one hp).Ne.symm
   by_cases hμ : μ Set.univ = 0
-  · rw [measure.measure_univ_eq_zero] at hμ 
+  · rw [measure.measure_univ_eq_zero] at hμ
     exact hμ.symm ▸ unif_integrable_zero_meas
   intro ε hε
   obtain ⟨C, hCpos, hC⟩ := h (ε / 2) (half_pos hε)
@@ -856,9 +856,9 @@ theorem unifIntegrable_of (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β
     filter_upwards [(Exists.choose_spec <| hf i).2] with x hx
     by_cases hfx : x ∈ {x | C ≤ ‖f i x‖₊}
     · rw [indicator_of_mem hfx, indicator_of_mem, hx]
-      rwa [mem_set_of, hx] at hfx 
+      rwa [mem_set_of, hx] at hfx
     · rw [indicator_of_not_mem hfx, indicator_of_not_mem]
-      rwa [mem_set_of, hx] at hfx 
+      rwa [mem_set_of, hx] at hfx
   refine' ⟨max C 1, lt_max_of_lt_right one_pos, fun i => le_trans (snorm_mono fun x => _) (hCg i)⟩
   rw [norm_indicator_eq_indicator_norm, norm_indicator_eq_indicator_norm]
   exact
@@ -925,7 +925,7 @@ theorem uniformIntegrable_finite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠
     rw [ENNReal.coe_toNNReal]
     · exact Finset.le_max' _ _ (Finset.mem_image.2 ⟨i, Finset.mem_univ _, rfl⟩)
     · refine' ne_of_lt ((Finset.max'_lt_iff _ _).2 fun y hy => _)
-      rw [Finset.mem_image] at hy 
+      rw [Finset.mem_image] at hy
       obtain ⟨i, -, rfl⟩ := hy
       exact hf i
   · exact ⟨0, fun i => False.elim <| hι <| Nonempty.intro i⟩
@@ -1024,9 +1024,9 @@ theorem uniformIntegrable_of [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ 
   filter_upwards [(Exists.choose_spec <| hf i).2] with x hx
   by_cases hfx : x ∈ {x | C ≤ ‖f i x‖₊}
   · rw [indicator_of_mem hfx, indicator_of_mem, hx]
-    rwa [mem_set_of, hx] at hfx 
+    rwa [mem_set_of, hx] at hfx
   · rw [indicator_of_not_mem hfx, indicator_of_not_mem]
-    rwa [mem_set_of, hx] at hfx 
+    rwa [mem_set_of, hx] at hfx
 #align measure_theory.uniform_integrable_of MeasureTheory.uniformIntegrable_of
 -/
 
@@ -1040,7 +1040,7 @@ theorem UniformIntegrable.spec' (hp : p ≠ 0) (hp' : p ≠ ∞) (hf : ∀ i, St
   obtain ⟨δ, hδpos, hδ⟩ := hfu hε
   obtain ⟨C, hC⟩ : ∃ C : ℝ≥0, ∀ i, μ {x | C ≤ ‖f i x‖₊} ≤ ENNReal.ofReal δ :=
     by
-    by_contra hcon; push_neg at hcon 
+    by_contra hcon; push_neg at hcon
     choose ℐ hℐ using hcon
     lift δ to ℝ≥0 using hδpos.le
     have : ∀ C : ℝ≥0, C • (δ : ℝ≥0∞) ^ (1 / p.to_real) ≤ snorm (f (ℐ C)) p μ :=
@@ -1050,7 +1050,7 @@ theorem UniformIntegrable.spec' (hp : p ≠ 0) (hp' : p ≠ ∞) (hf : ∀ i, St
         C • (δ : ℝ≥0∞) ^ (1 / p.to_real) ≤ C • μ {x | C ≤ ‖f (ℐ C) x‖₊} ^ (1 / p.to_real) :=
           by
           rw [ENNReal.smul_def, ENNReal.smul_def, smul_eq_mul, smul_eq_mul]
-          simp_rw [ENNReal.ofReal_coe_nnreal] at hℐ 
+          simp_rw [ENNReal.ofReal_coe_nnreal] at hℐ
           refine'
             mul_le_mul' le_rfl
               (ENNReal.rpow_le_rpow (hℐ C).le (one_div_nonneg.2 ENNReal.toReal_nonneg))
@@ -1066,7 +1066,7 @@ theorem UniformIntegrable.spec' (hp : p ≠ 0) (hp' : p ≠ ∞) (hf : ∀ i, St
     rw [ENNReal.coe_rpow_of_nonneg _ (one_div_nonneg.2 ENNReal.toReal_nonneg), ← ENNReal.coe_smul,
       smul_eq_mul, mul_assoc, NNReal.inv_rpow,
       inv_mul_cancel (NNReal.rpow_pos (NNReal.coe_pos.1 hδpos)).Ne.symm, mul_one, ENNReal.coe_mul, ←
-      NNReal.inv_rpow] at this 
+      NNReal.inv_rpow] at this
     refine'
       (lt_of_le_of_lt (le_trans (hM <| ℐ <| 2 * max M 1 * δ⁻¹ ^ (1 / p.to_real)) (le_max_left M 1))
             (lt_of_lt_of_le _ this)).Ne
@@ -1090,9 +1090,9 @@ theorem UniformIntegrable.spec (hp : p ≠ 0) (hp' : p ≠ ∞) (hfu : UniformIn
   filter_upwards [(Exists.choose_spec <| hfu.1 i).2] with x hx
   by_cases hfx : x ∈ {x | C ≤ ‖f i x‖₊}
   · rw [indicator_of_mem hfx, indicator_of_mem, hx]
-    rwa [mem_set_of, hx] at hfx 
+    rwa [mem_set_of, hx] at hfx
   · rw [indicator_of_not_mem hfx, indicator_of_not_mem]
-    rwa [mem_set_of, hx] at hfx 
+    rwa [mem_set_of, hx] at hfx
 #align measure_theory.uniform_integrable.spec MeasureTheory.UniformIntegrable.spec
 -/
 
@@ -1139,7 +1139,7 @@ theorem uniformIntegrable_average_real (hp : 1 ≤ p) {f : ℕ → α → ℝ} (
     · refine' (ENNReal.mul_le_mul_left hn ENNReal.coe_ne_top).2 _
       conv_rhs => rw [← Finset.card_range n]
       exact Finset.sum_le_card_nsmul _ _ _ fun i hi => hδ₂ _ _ hs hle
-    · simp only [ENNReal.coe_eq_zero, inv_eq_zero, Nat.cast_eq_zero] at hn 
+    · simp only [ENNReal.coe_eq_zero, inv_eq_zero, Nat.cast_eq_zero] at hn
       rw [nsmul_eq_mul, ← mul_assoc, ENNReal.coe_inv, ENNReal.coe_nat,
         ENNReal.inv_mul_cancel _ (ENNReal.nat_ne_top _), one_mul]
       · exact le_rfl
@@ -1159,7 +1159,7 @@ theorem uniformIntegrable_average_real (hp : 1 ≤ p) {f : ℕ → α → ℝ} (
     · refine' (ENNReal.mul_le_mul_left hn ENNReal.coe_ne_top).2 _
       conv_rhs => rw [← Finset.card_range n]
       exact Finset.sum_le_card_nsmul _ _ _ fun i hi => hC i
-    · simp only [ENNReal.coe_eq_zero, inv_eq_zero, Nat.cast_eq_zero] at hn 
+    · simp only [ENNReal.coe_eq_zero, inv_eq_zero, Nat.cast_eq_zero] at hn
       rw [nsmul_eq_mul, ← mul_assoc, ENNReal.coe_inv, ENNReal.coe_nat,
         ENNReal.inv_mul_cancel _ (ENNReal.nat_ne_top _), one_mul]
       · exact le_rfl

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -262,7 +262,7 @@ theorem Memℒp.integral_indicator_norm_ge_nonneg_le (hf : Memℒp f 1 μ) {ε :
   refine' ⟨M, hM_pos, (le_of_eq _).trans hfM⟩
   refine' lintegral_congr_ae _
   filter_upwards [hf.1.ae_eq_mk] with x hx
-  simp only [indicator_apply, coe_nnnorm, mem_set_of_eq, ENNReal.coe_eq_coe, hx.symm]
+  simp only [indicator_apply, coe_nnnorm, mem_set_of_eq, ENNReal.coe_inj, hx.symm]
 #align measure_theory.mem_ℒp.integral_indicator_norm_ge_nonneg_le MeasureTheory.Memℒp.integral_indicator_norm_ge_nonneg_le
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -325,7 +325,7 @@ theorem Memℒp.snorm_indicator_norm_ge_le (hf : Memℒp f p μ) (hmeas : Strong
     nnnorm_indicator_eq_indicator_nnnorm]
   have hiff : M ^ (1 / p.to_real) ≤ ‖f x‖₊ ↔ M ≤ ‖‖f x‖ ^ p.to_real‖₊ := by
     rw [coe_nnnorm, coe_nnnorm, Real.norm_rpow_of_nonneg (norm_nonneg _), norm_norm, ←
-      Real.rpow_le_rpow_iff hM' (Real.rpow_nonneg_of_nonneg (norm_nonneg _) _)
+      Real.rpow_le_rpow_iff hM' (Real.rpow_nonneg (norm_nonneg _) _)
         (one_div_pos.2 <| ENNReal.toReal_pos hp_ne_zero hp_ne_top),
       ← Real.rpow_mul (norm_nonneg _),
       mul_one_div_cancel (ENNReal.toReal_pos hp_ne_zero hp_ne_top).Ne.symm, Real.rpow_one]

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -1123,7 +1123,7 @@ theorem uniformIntegrable_average_real (hp : 1 ≤ p) {f : ℕ → α → ℝ} (
         (ae_strongly_measurable_const : ae_strongly_measurable (fun x => (↑n : ℝ)⁻¹) μ)
   · obtain ⟨δ, hδ₁, hδ₂⟩ := hf₂ hε
     refine' ⟨δ, hδ₁, fun n s hs hle => _⟩
-    simp_rw [div_eq_mul_inv, Finset.sum_mul, Set.indicator_finset_sum]
+    simp_rw [div_eq_mul_inv, Finset.sum_mul, Finset.indicator_sum]
     refine' le_trans (snorm_sum_le (fun i hi => ((hf₁ i).mul_const (↑n)⁻¹).indicator hs) hp) _
     have : ∀ i, s.indicator (f i * (↑n)⁻¹) = (↑n : ℝ)⁻¹ • s.indicator (f i) :=
       by

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -1110,9 +1110,9 @@ theorem uniformIntegrable_iff [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ 
 #align measure_theory.uniform_integrable_iff MeasureTheory.uniformIntegrable_iff
 -/
 
-#print MeasureTheory.uniformIntegrable_average /-
+#print MeasureTheory.uniformIntegrable_average_real /-
 /-- The averaging of a uniformly integrable sequence is also uniformly integrable. -/
-theorem uniformIntegrable_average (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf : UniformIntegrable f p μ) :
+theorem uniformIntegrable_average_real (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf : UniformIntegrable f p μ) :
     UniformIntegrable (fun n => (∑ i in Finset.range n, f i) / n) p μ :=
   by
   obtain ⟨hf₁, hf₂, hf₃⟩ := hf
@@ -1164,7 +1164,7 @@ theorem uniformIntegrable_average (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf :
         ENNReal.inv_mul_cancel _ (ENNReal.nat_ne_top _), one_mul]
       · exact le_rfl
       all_goals simpa only [Ne.def, Nat.cast_eq_zero]
-#align measure_theory.uniform_integrable_average MeasureTheory.uniformIntegrable_average
+#align measure_theory.uniform_integrable_average MeasureTheory.uniformIntegrable_average_real
 -/
 
 end UniformIntegrable

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,8 +3,8 @@ Copyright (c) 2022 Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
 -/
-import Mathbin.MeasureTheory.Function.ConvergenceInMeasure
-import Mathbin.MeasureTheory.Function.L1Space
+import MeasureTheory.Function.ConvergenceInMeasure
+import MeasureTheory.Function.L1Space
 
 #align_import measure_theory.function.uniform_integrable from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
 
@@ -359,7 +359,7 @@ theorem Memℒp.snorm_indicator_norm_ge_pos_le (hf : Memℒp f p μ) (hmeas : St
 
 end
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], [], []]: ./././Mathport/Syntax/Translate/Basic.lean:349:22: unsupported: parse error @ arg 0: next failed, no more args -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], [], []]: ./././Mathport/Syntax/Translate/Basic.lean:354:22: unsupported: parse error @ arg 0: next failed, no more args -/
 #print MeasureTheory.snorm_indicator_le_of_bound /-
 theorem snorm_indicator_le_of_bound {f : α → β} (hp_top : p ≠ ∞) {ε : ℝ} (hε : 0 < ε) {M : ℝ}
     (hf : ∀ x, ‖f x‖ < M) :
@@ -382,7 +382,7 @@ theorem snorm_indicator_le_of_bound {f : α → β} (hp_top : p ≠ ∞) {ε : 
   have haebdd : ∀ᵐ x ∂μ.restrict s, ‖f x‖ ≤ M :=
     by
     trace
-      "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], [], []]: ./././Mathport/Syntax/Translate/Basic.lean:349:22: unsupported: parse error @ arg 0: next failed, no more args"
+      "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], [], []]: ./././Mathport/Syntax/Translate/Basic.lean:354:22: unsupported: parse error @ arg 0: next failed, no more args"
     exact fun x => (hf x).le
   refine' le_trans (snorm_le_of_ae_bound haebdd) _
   rw [measure.restrict_apply MeasurableSet.univ, univ_inter, ←

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
-
-! This file was ported from Lean 3 source module measure_theory.function.uniform_integrable
-! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Function.ConvergenceInMeasure
 import Mathbin.MeasureTheory.Function.L1Space
 
+#align_import measure_theory.function.uniform_integrable from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
+
 /-!
 # Uniform integrability
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -87,22 +87,28 @@ def UniformIntegrable {m : MeasurableSpace α} (f : ι → α → β) (p : ℝ
 
 namespace UniformIntegrable
 
+#print MeasureTheory.UniformIntegrable.aeStronglyMeasurable /-
 protected theorem aeStronglyMeasurable {f : ι → α → β} {p : ℝ≥0∞} (hf : UniformIntegrable f p μ)
     (i : ι) : AEStronglyMeasurable (f i) μ :=
   hf.1 i
 #align measure_theory.uniform_integrable.ae_strongly_measurable MeasureTheory.UniformIntegrable.aeStronglyMeasurable
+-/
 
+#print MeasureTheory.UniformIntegrable.unifIntegrable /-
 protected theorem unifIntegrable {f : ι → α → β} {p : ℝ≥0∞} (hf : UniformIntegrable f p μ) :
     UnifIntegrable f p μ :=
   hf.2.1
 #align measure_theory.uniform_integrable.unif_integrable MeasureTheory.UniformIntegrable.unifIntegrable
+-/
 
+#print MeasureTheory.UniformIntegrable.memℒp /-
 protected theorem memℒp {f : ι → α → β} {p : ℝ≥0∞} (hf : UniformIntegrable f p μ) (i : ι) :
     Memℒp (f i) p μ :=
   ⟨hf.1 i,
     let ⟨_, _, hC⟩ := hf.2
     lt_of_le_of_lt (hC i) ENNReal.coe_lt_top⟩
 #align measure_theory.uniform_integrable.mem_ℒp MeasureTheory.UniformIntegrable.memℒp
+-/
 
 end UniformIntegrable
 
@@ -117,6 +123,7 @@ namespace UnifIntegrable
 
 variable {f g : ι → α → β} {p : ℝ≥0∞}
 
+#print MeasureTheory.UnifIntegrable.add /-
 protected theorem add (hf : UnifIntegrable f p μ) (hg : UnifIntegrable g p μ) (hp : 1 ≤ p)
     (hf_meas : ∀ i, AEStronglyMeasurable (f i) μ) (hg_meas : ∀ i, AEStronglyMeasurable (g i) μ) :
     UnifIntegrable (f + g) p μ := by
@@ -134,17 +141,23 @@ protected theorem add (hf : UnifIntegrable f p μ) (hg : UnifIntegrable g p μ)
     add_le_add (hfδ₁ i s hs (hμs.trans (ENNReal.ofReal_le_ofReal (min_le_left _ _))))
       (hgδ₂ i s hs (hμs.trans (ENNReal.ofReal_le_ofReal (min_le_right _ _))))
 #align measure_theory.unif_integrable.add MeasureTheory.UnifIntegrable.add
+-/
 
+#print MeasureTheory.UnifIntegrable.neg /-
 protected theorem neg (hf : UnifIntegrable f p μ) : UnifIntegrable (-f) p μ := by
   simp_rw [unif_integrable, Pi.neg_apply, indicator_neg', snorm_neg]; exact hf
 #align measure_theory.unif_integrable.neg MeasureTheory.UnifIntegrable.neg
+-/
 
+#print MeasureTheory.UnifIntegrable.sub /-
 protected theorem sub (hf : UnifIntegrable f p μ) (hg : UnifIntegrable g p μ) (hp : 1 ≤ p)
     (hf_meas : ∀ i, AEStronglyMeasurable (f i) μ) (hg_meas : ∀ i, AEStronglyMeasurable (g i) μ) :
     UnifIntegrable (f - g) p μ := by rw [sub_eq_add_neg];
   exact hf.add hg.neg hp hf_meas fun i => (hg_meas i).neg
 #align measure_theory.unif_integrable.sub MeasureTheory.UnifIntegrable.sub
+-/
 
+#print MeasureTheory.UnifIntegrable.ae_eq /-
 protected theorem ae_eq (hf : UnifIntegrable f p μ) (hfg : ∀ n, f n =ᵐ[μ] g n) :
     UnifIntegrable g p μ := by
   intro ε hε
@@ -153,18 +166,24 @@ protected theorem ae_eq (hf : UnifIntegrable f p μ) (hfg : ∀ n, f n =ᵐ[μ]
   filter_upwards [hfg n] with x hx
   simp_rw [indicator_apply, hx]
 #align measure_theory.unif_integrable.ae_eq MeasureTheory.UnifIntegrable.ae_eq
+-/
 
 end UnifIntegrable
 
+#print MeasureTheory.unifIntegrable_zero_meas /-
 theorem unifIntegrable_zero_meas [MeasurableSpace α] {p : ℝ≥0∞} {f : ι → α → β} :
     UnifIntegrable f p (0 : Measure α) := fun ε hε => ⟨1, one_pos, fun i s hs hμs => by simp⟩
 #align measure_theory.unif_integrable_zero_meas MeasureTheory.unifIntegrable_zero_meas
+-/
 
+#print MeasureTheory.unifIntegrable_congr_ae /-
 theorem unifIntegrable_congr_ae {p : ℝ≥0∞} {f g : ι → α → β} (hfg : ∀ n, f n =ᵐ[μ] g n) :
     UnifIntegrable f p μ ↔ UnifIntegrable g p μ :=
   ⟨fun hf => hf.ae_eq hfg, fun hg => hg.ae_eq fun n => (hfg n).symm⟩
 #align measure_theory.unif_integrable_congr_ae MeasureTheory.unifIntegrable_congr_ae
+-/
 
+#print MeasureTheory.tendsto_indicator_ge /-
 theorem tendsto_indicator_ge (f : α → β) (x : α) :
     Tendsto (fun M : ℕ => {x | (M : ℝ) ≤ ‖f x‖₊}.indicator f x) atTop (𝓝 0) :=
   by
@@ -176,6 +195,7 @@ theorem tendsto_indicator_ge (f : α → β) (x : α) :
   norm_cast
   rwa [ge_iff_le, coe_nnnorm] at hn 
 #align measure_theory.tendsto_indicator_ge MeasureTheory.tendsto_indicator_ge
+-/
 
 variable (μ) {p : ℝ≥0∞}
 
@@ -183,6 +203,7 @@ section
 
 variable {f : α → β}
 
+#print MeasureTheory.Memℒp.integral_indicator_norm_ge_le /-
 /-- This lemma is weaker than `measure_theory.mem_ℒp.integral_indicator_norm_ge_nonneg_le`
 as the latter provides `0 ≤ M` and does not require the measurability of `f`. -/
 theorem Memℒp.integral_indicator_norm_ge_le (hf : Memℒp f 1 μ) (hmeas : StronglyMeasurable f)
@@ -221,7 +242,9 @@ theorem Memℒp.integral_indicator_norm_ge_le (hf : Memℒp f 1 μ) (hmeas : Str
       · exact norm_nonneg _
       · assumption
 #align measure_theory.mem_ℒp.integral_indicator_norm_ge_le MeasureTheory.Memℒp.integral_indicator_norm_ge_le
+-/
 
+#print MeasureTheory.Memℒp.integral_indicator_norm_ge_nonneg_le_of_meas /-
 /-- This lemma is superceded by `measure_theory.mem_ℒp.integral_indicator_norm_ge_nonneg_le`
 which does not require measurability. -/
 theorem Memℒp.integral_indicator_norm_ge_nonneg_le_of_meas (hf : Memℒp f 1 μ)
@@ -230,7 +253,9 @@ theorem Memℒp.integral_indicator_norm_ge_nonneg_le_of_meas (hf : Memℒp f 1 
   let ⟨M, hM⟩ := hf.integral_indicator_norm_ge_le μ hmeas hε
   ⟨max M 0, le_max_right _ _, by simpa⟩
 #align measure_theory.mem_ℒp.integral_indicator_norm_ge_nonneg_le_of_meas MeasureTheory.Memℒp.integral_indicator_norm_ge_nonneg_le_of_meas
+-/
 
+#print MeasureTheory.Memℒp.integral_indicator_norm_ge_nonneg_le /-
 theorem Memℒp.integral_indicator_norm_ge_nonneg_le (hf : Memℒp f 1 μ) {ε : ℝ} (hε : 0 < ε) :
     ∃ M : ℝ, 0 ≤ M ∧ ∫⁻ x, ‖{x | M ≤ ‖f x‖₊}.indicator f x‖₊ ∂μ ≤ ENNReal.ofReal ε :=
   by
@@ -242,7 +267,9 @@ theorem Memℒp.integral_indicator_norm_ge_nonneg_le (hf : Memℒp f 1 μ) {ε :
   filter_upwards [hf.1.ae_eq_mk] with x hx
   simp only [indicator_apply, coe_nnnorm, mem_set_of_eq, ENNReal.coe_eq_coe, hx.symm]
 #align measure_theory.mem_ℒp.integral_indicator_norm_ge_nonneg_le MeasureTheory.Memℒp.integral_indicator_norm_ge_nonneg_le
+-/
 
+#print MeasureTheory.Memℒp.snormEssSup_indicator_norm_ge_eq_zero /-
 theorem Memℒp.snormEssSup_indicator_norm_ge_eq_zero (hf : Memℒp f ∞ μ)
     (hmeas : StronglyMeasurable f) : ∃ M : ℝ, snormEssSup ({x | M ≤ ‖f x‖₊}.indicator f) μ = 0 :=
   by
@@ -270,7 +297,9 @@ theorem Memℒp.snormEssSup_indicator_norm_ge_eq_zero (hf : Memℒp f ∞ μ)
   rw [this, snorm_ess_sup_measure_zero]
   exact measurableSet_le measurable_const hmeas.nnnorm.measurable.subtype_coe
 #align measure_theory.mem_ℒp.snorm_ess_sup_indicator_norm_ge_eq_zero MeasureTheory.Memℒp.snormEssSup_indicator_norm_ge_eq_zero
+-/
 
+#print MeasureTheory.Memℒp.snorm_indicator_norm_ge_le /-
 /- This lemma is slightly weaker than `measure_theory.mem_ℒp.snorm_indicator_norm_ge_pos_le` as the
 latter provides `0 < M`. -/
 theorem Memℒp.snorm_indicator_norm_ge_le (hf : Memℒp f p μ) (hmeas : StronglyMeasurable f) {ε : ℝ}
@@ -312,7 +341,9 @@ theorem Memℒp.snorm_indicator_norm_ge_le (hf : Memℒp f p μ) (hmeas : Strong
     · change ¬_ ≤ _
       rwa [← hiff]
 #align measure_theory.mem_ℒp.snorm_indicator_norm_ge_le MeasureTheory.Memℒp.snorm_indicator_norm_ge_le
+-/
 
+#print MeasureTheory.Memℒp.snorm_indicator_norm_ge_pos_le /-
 /-- This lemma implies that a single function is uniformly integrable (in the probability sense). -/
 theorem Memℒp.snorm_indicator_norm_ge_pos_le (hf : Memℒp f p μ) (hmeas : StronglyMeasurable f)
     {ε : ℝ} (hε : 0 < ε) :
@@ -327,10 +358,12 @@ theorem Memℒp.snorm_indicator_norm_ge_pos_le (hf : Memℒp f p μ) (hmeas : St
   -- removing the `change` breaks the proof!
   exact (max_le_iff.1 hx).1
 #align measure_theory.mem_ℒp.snorm_indicator_norm_ge_pos_le MeasureTheory.Memℒp.snorm_indicator_norm_ge_pos_le
+-/
 
 end
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], [], []]: ./././Mathport/Syntax/Translate/Basic.lean:349:22: unsupported: parse error @ arg 0: next failed, no more args -/
+#print MeasureTheory.snorm_indicator_le_of_bound /-
 theorem snorm_indicator_le_of_bound {f : α → β} (hp_top : p ≠ ∞) {ε : ℝ} (hε : 0 < ε) {M : ℝ}
     (hf : ∀ x, ‖f x‖ < M) :
     ∃ (δ : ℝ) (hδ : 0 < δ),
@@ -364,11 +397,13 @@ theorem snorm_indicator_le_of_bound {f : α → β} (hp_top : p ≠ ∞) {ε : 
     exact le_rfl
   · simpa only [ENNReal.ofReal_eq_zero, not_le, Ne.def]
 #align measure_theory.snorm_indicator_le_of_bound MeasureTheory.snorm_indicator_le_of_bound
+-/
 
 section
 
 variable {f : α → β}
 
+#print MeasureTheory.Memℒp.snorm_indicator_le' /-
 /-- Auxiliary lemma for `measure_theory.mem_ℒp.snorm_indicator_le`. -/
 theorem Memℒp.snorm_indicator_le' (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) (hf : Memℒp f p μ)
     (hmeas : StronglyMeasurable f) {ε : ℝ} (hε : 0 < ε) :
@@ -407,7 +442,9 @@ theorem Memℒp.snorm_indicator_le' (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) (hf
     split_ifs
     exacts [h, hMpos]
 #align measure_theory.mem_ℒp.snorm_indicator_le' MeasureTheory.Memℒp.snorm_indicator_le'
+-/
 
+#print MeasureTheory.Memℒp.snorm_indicator_le_of_meas /-
 /-- This lemma is superceded by `measure_theory.mem_ℒp.snorm_indicator_le` which does not require
 measurability on `f`. -/
 theorem Memℒp.snorm_indicator_le_of_meas (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) (hf : Memℒp f p μ)
@@ -422,7 +459,9 @@ theorem Memℒp.snorm_indicator_le_of_meas (hp_one : 1 ≤ p) (hp_top : p ≠ 
       ENNReal.mul_div_cancel'] <;>
     norm_num
 #align measure_theory.mem_ℒp.snorm_indicator_le_of_meas MeasureTheory.Memℒp.snorm_indicator_le_of_meas
+-/
 
+#print MeasureTheory.Memℒp.snorm_indicator_le /-
 theorem Memℒp.snorm_indicator_le (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) (hf : Memℒp f p μ) {ε : ℝ}
     (hε : 0 < ε) :
     ∃ (δ : ℝ) (hδ : 0 < δ),
@@ -437,7 +476,9 @@ theorem Memℒp.snorm_indicator_le (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) (hf :
   rw [snorm_indicator_eq_snorm_restrict hs, snorm_indicator_eq_snorm_restrict hs]
   refine' snorm_congr_ae heq.restrict
 #align measure_theory.mem_ℒp.snorm_indicator_le MeasureTheory.Memℒp.snorm_indicator_le
+-/
 
+#print MeasureTheory.unifIntegrable_const /-
 /-- A constant function is uniformly integrable. -/
 theorem unifIntegrable_const {g : α → β} (hp : 1 ≤ p) (hp_ne_top : p ≠ ∞) (hg : Memℒp g p μ) :
     UnifIntegrable (fun n : ι => g) p μ := by
@@ -445,7 +486,9 @@ theorem unifIntegrable_const {g : α → β} (hp : 1 ≤ p) (hp_ne_top : p ≠ 
   obtain ⟨δ, hδ_pos, hgδ⟩ := hg.snorm_indicator_le μ hp hp_ne_top hε
   exact ⟨δ, hδ_pos, fun i => hgδ⟩
 #align measure_theory.unif_integrable_const MeasureTheory.unifIntegrable_const
+-/
 
+#print MeasureTheory.unifIntegrable_subsingleton /-
 /-- A single function is uniformly integrable. -/
 theorem unifIntegrable_subsingleton [Subsingleton ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞)
     {f : ι → α → β} (hf : ∀ i, Memℒp (f i) p μ) : UnifIntegrable f p μ :=
@@ -458,7 +501,9 @@ theorem unifIntegrable_subsingleton [Subsingleton ι] (hp_one : 1 ≤ p) (hp_top
     convert hδ s hs hμs
   · exact ⟨1, zero_lt_one, fun i => False.elim <| hι <| Nonempty.intro i⟩
 #align measure_theory.unif_integrable_subsingleton MeasureTheory.unifIntegrable_subsingleton
+-/
 
+#print MeasureTheory.unifIntegrable_fin /-
 /-- This lemma is less general than `measure_theory.unif_integrable_fintype` which applies to
 all sequences indexed by a finite type. -/
 theorem unifIntegrable_fin (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) {n : ℕ} {f : Fin n → α → β}
@@ -484,7 +529,9 @@ theorem unifIntegrable_fin (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) {n : ℕ} {f
       rw [not_lt] at hi 
       simp [← le_antisymm hi' hi]
 #align measure_theory.unif_integrable_fin MeasureTheory.unifIntegrable_fin
+-/
 
+#print MeasureTheory.unifIntegrable_finite /-
 /-- A finite sequence of Lp functions is uniformly integrable. -/
 theorem unifIntegrable_finite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) {f : ι → α → β}
     (hf : ∀ i, Memℒp (f i) p μ) : UnifIntegrable f p μ :=
@@ -499,9 +546,11 @@ theorem unifIntegrable_finite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞
   simp_rw [hgeq, Function.comp_apply, Equiv.symm_apply_apply] at hδ 
   assumption
 #align measure_theory.unif_integrable_finite MeasureTheory.unifIntegrable_finite
+-/
 
 end
 
+#print MeasureTheory.snorm_sub_le_of_dist_bdd /-
 theorem snorm_sub_le_of_dist_bdd {p : ℝ≥0∞} (hp' : p ≠ ∞) {s : Set α} (hs : measurable_set[m] s)
     {f g : α → β} {c : ℝ} (hc : 0 ≤ c) (hf : ∀ x ∈ s, dist (f x) (g x) ≤ c) :
     snorm (s.indicator (f - g)) p μ ≤ ENNReal.ofReal c * μ s ^ (1 / p.toReal) :=
@@ -521,7 +570,9 @@ theorem snorm_sub_le_of_dist_bdd {p : ℝ≥0∞} (hp' : p ≠ ∞) {s : Set α}
   refine' mul_le_mul_right' (le_of_eq _) _
   rw [← ofReal_norm_eq_coe_nnnorm, Real.norm_eq_abs, abs_of_nonneg hc]
 #align measure_theory.snorm_sub_le_of_dist_bdd MeasureTheory.snorm_sub_le_of_dist_bdd
+-/
 
+#print MeasureTheory.tendsto_Lp_of_tendsto_ae_of_meas /-
 /-- A sequence of uniformly integrable functions which converges μ-a.e. converges in Lp. -/
 theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
     {f : ℕ → α → β} {g : α → β} (hf : ∀ n, StronglyMeasurable (f n)) (hg : StronglyMeasurable g)
@@ -606,7 +657,9 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp
   rw [snorm_neg, ← ENNReal.add_thirds ε, ← sub_eq_add_neg]
   exact add_le_add_three hnf hng hlt
 #align measure_theory.tendsto_Lp_of_tendsto_ae_of_meas MeasureTheory.tendsto_Lp_of_tendsto_ae_of_meas
+-/
 
+#print MeasureTheory.tendsto_Lp_of_tendsto_ae /-
 /-- A sequence of uniformly integrable functions which converges μ-a.e. converges in Lp. -/
 theorem tendsto_Lp_of_tendsto_ae [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ℕ → α → β}
     {g : α → β} (hf : ∀ n, AEStronglyMeasurable (f n) μ) (hg : Memℒp g p μ)
@@ -630,9 +683,11 @@ theorem tendsto_Lp_of_tendsto_ae [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p 
   ext1 n
   exact (hxf_eq n).symm
 #align measure_theory.tendsto_Lp_of_tendsto_ae MeasureTheory.tendsto_Lp_of_tendsto_ae
+-/
 
 variable {f : ℕ → α → β} {g : α → β}
 
+#print MeasureTheory.unifIntegrable_of_tendsto_Lp_zero /-
 theorem unifIntegrable_of_tendsto_Lp_zero (hp : 1 ≤ p) (hp' : p ≠ ∞) (hf : ∀ n, Memℒp (f n) p μ)
     (hf_tendsto : Tendsto (fun n => snorm (f n) p μ) atTop (𝓝 0)) : UnifIntegrable f p μ :=
   by
@@ -647,7 +702,9 @@ theorem unifIntegrable_of_tendsto_Lp_zero (hp : 1 ≤ p) (hp' : p ≠ ∞) (hf :
   · exact hδ₁ ⟨n, hn⟩ s hs hμs
   · exact (snorm_indicator_le _).trans (hN n (not_lt.1 hn))
 #align measure_theory.unif_integrable_of_tendsto_Lp_zero MeasureTheory.unifIntegrable_of_tendsto_Lp_zero
+-/
 
+#print MeasureTheory.unifIntegrable_of_tendsto_Lp /-
 /-- Convergence in Lp implies uniform integrability. -/
 theorem unifIntegrable_of_tendsto_Lp (hp : 1 ≤ p) (hp' : p ≠ ∞) (hf : ∀ n, Memℒp (f n) p μ)
     (hg : Memℒp g p μ) (hfg : Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0)) :
@@ -661,7 +718,9 @@ theorem unifIntegrable_of_tendsto_Lp (hp : 1 ≤ p) (hp' : p ≠ ∞) (hf : ∀
   · exact unif_integrable_const μ hp hp' hg
   · exact unif_integrable_of_tendsto_Lp_zero μ hp hp' (fun n => (hf n).sub hg) hfg
 #align measure_theory.unif_integrable_of_tendsto_Lp MeasureTheory.unifIntegrable_of_tendsto_Lp
+-/
 
+#print MeasureTheory.tendsto_Lp_of_tendstoInMeasure /-
 /-- Forward direction of Vitali's convergence theorem: if `f` is a sequence of uniformly integrable
 functions that converge in measure to some function `g` in a finite measure space, then `f`
 converge in Lp to `g`. -/
@@ -679,7 +738,9 @@ theorem tendsto_Lp_of_tendstoInMeasure [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp'
           ⟨δ, hδ, fun i s hs hμs => hδ' _ s hs hμs⟩)
         hms'⟩
 #align measure_theory.tendsto_Lp_of_tendsto_in_measure MeasureTheory.tendsto_Lp_of_tendstoInMeasure
+-/
 
+#print MeasureTheory.tendstoInMeasure_iff_tendsto_Lp /-
 /-- **Vitali's convergence theorem**: A sequence of functions `f` converges to `g` in Lp if and
 only if it is uniformly integrable and converges to `g` in measure. -/
 theorem tendstoInMeasure_iff_tendsto_Lp [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
@@ -691,7 +752,9 @@ theorem tendstoInMeasure_iff_tendsto_Lp [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp'
         (fun n => (hf n).AEStronglyMeasurable) hg.AEStronglyMeasurable h,
       unifIntegrable_of_tendsto_Lp μ hp hp' hf hg h⟩⟩
 #align measure_theory.tendsto_in_measure_iff_tendsto_Lp MeasureTheory.tendstoInMeasure_iff_tendsto_Lp
+-/
 
+#print MeasureTheory.unifIntegrable_of' /-
 /-- This lemma is superceded by `unif_integrable_of` which do not require `C` to be positive. -/
 theorem unifIntegrable_of' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β}
     (hf : ∀ i, StronglyMeasurable (f i))
@@ -775,7 +838,9 @@ theorem unifIntegrable_of' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → 
       rw [← ENNReal.ofReal_add (half_pos hε).le (half_pos hε).le, add_halves]
       exact le_rfl
 #align measure_theory.unif_integrable_of' MeasureTheory.unifIntegrable_of'
+-/
 
+#print MeasureTheory.unifIntegrable_of /-
 theorem unifIntegrable_of (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β}
     (hf : ∀ i, AEStronglyMeasurable (f i) μ)
     (h :
@@ -803,6 +868,7 @@ theorem unifIntegrable_of (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β
     indicator_le_indicator_of_subset (fun x hx => le_trans (le_max_left _ _) hx)
       (fun _ => norm_nonneg _) _
 #align measure_theory.unif_integrable_of MeasureTheory.unifIntegrable_of
+-/
 
 end UnifIntegrable
 
@@ -821,11 +887,14 @@ In this section, we will develope some API for `uniform_integrable` and prove th
 
 variable {p : ℝ≥0∞} {f : ι → α → β}
 
+#print MeasureTheory.uniformIntegrable_zero_meas /-
 theorem uniformIntegrable_zero_meas [MeasurableSpace α] : UniformIntegrable f p (0 : Measure α) :=
   ⟨fun n => aestronglyMeasurable_zero_measure _, unifIntegrable_zero_meas, 0, fun i =>
     snorm_measure_zero.le⟩
 #align measure_theory.uniform_integrable_zero_meas MeasureTheory.uniformIntegrable_zero_meas
+-/
 
+#print MeasureTheory.UniformIntegrable.ae_eq /-
 theorem UniformIntegrable.ae_eq {g : ι → α → β} (hf : UniformIntegrable f p μ)
     (hfg : ∀ n, f n =ᵐ[μ] g n) : UniformIntegrable g p μ :=
   by
@@ -834,12 +903,16 @@ theorem UniformIntegrable.ae_eq {g : ι → α → β} (hf : UniformIntegrable f
   rw [← snorm_congr_ae (hfg i)]
   exact hC i
 #align measure_theory.uniform_integrable.ae_eq MeasureTheory.UniformIntegrable.ae_eq
+-/
 
+#print MeasureTheory.uniformIntegrable_congr_ae /-
 theorem uniformIntegrable_congr_ae {g : ι → α → β} (hfg : ∀ n, f n =ᵐ[μ] g n) :
     UniformIntegrable f p μ ↔ UniformIntegrable g p μ :=
   ⟨fun h => h.ae_eq hfg, fun h => h.ae_eq fun i => (hfg i).symm⟩
 #align measure_theory.uniform_integrable_congr_ae MeasureTheory.uniformIntegrable_congr_ae
+-/
 
+#print MeasureTheory.uniformIntegrable_finite /-
 /-- A finite sequence of Lp functions is uniformly integrable in the probability sense. -/
 theorem uniformIntegrable_finite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞)
     (hf : ∀ i, Memℒp (f i) p μ) : UniformIntegrable f p μ :=
@@ -860,20 +933,26 @@ theorem uniformIntegrable_finite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠
       exact hf i
   · exact ⟨0, fun i => False.elim <| hι <| Nonempty.intro i⟩
 #align measure_theory.uniform_integrable_finite MeasureTheory.uniformIntegrable_finite
+-/
 
+#print MeasureTheory.uniformIntegrable_subsingleton /-
 /-- A single function is uniformly integrable in the probability sense. -/
 theorem uniformIntegrable_subsingleton [Subsingleton ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞)
     (hf : ∀ i, Memℒp (f i) p μ) : UniformIntegrable f p μ :=
   uniformIntegrable_finite hp_one hp_top hf
 #align measure_theory.uniform_integrable_subsingleton MeasureTheory.uniformIntegrable_subsingleton
+-/
 
+#print MeasureTheory.uniformIntegrable_const /-
 /-- A constant sequence of functions is uniformly integrable in the probability sense. -/
 theorem uniformIntegrable_const {g : α → β} (hp : 1 ≤ p) (hp_ne_top : p ≠ ∞) (hg : Memℒp g p μ) :
     UniformIntegrable (fun n : ι => g) p μ :=
   ⟨fun i => hg.1, unifIntegrable_const μ hp hp_ne_top hg,
     ⟨(snorm g p μ).toNNReal, fun i => le_of_eq (ENNReal.coe_toNNReal hg.2.Ne).symm⟩⟩
 #align measure_theory.uniform_integrable_const MeasureTheory.uniformIntegrable_const
+-/
 
+#print MeasureTheory.uniformIntegrable_of' /-
 /-- This lemma is superceded by `uniform_integrable_of` which only requires
 `ae_strongly_measurable`. -/
 theorem uniformIntegrable_of' [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
@@ -927,7 +1006,9 @@ theorem uniformIntegrable_of' [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ 
                 (measure_lt_top _ _).Ne),
             ENNReal.one_ne_top⟩
 #align measure_theory.uniform_integrable_of' MeasureTheory.uniformIntegrable_of'
+-/
 
+#print MeasureTheory.uniformIntegrable_of /-
 /-- A sequene of functions `(fₙ)` is uniformly integrable in the probability sense if for all
 `ε > 0`, there exists some `C` such that `∫ x in {|fₙ| ≥ C}, fₙ x ∂μ ≤ ε` for all `n`. -/
 theorem uniformIntegrable_of [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
@@ -950,7 +1031,9 @@ theorem uniformIntegrable_of [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ 
   · rw [indicator_of_not_mem hfx, indicator_of_not_mem]
     rwa [mem_set_of, hx] at hfx 
 #align measure_theory.uniform_integrable_of MeasureTheory.uniformIntegrable_of
+-/
 
+#print MeasureTheory.UniformIntegrable.spec' /-
 /-- This lemma is superceded by `uniform_integrable.spec` which does not require measurability. -/
 theorem UniformIntegrable.spec' (hp : p ≠ 0) (hp' : p ≠ ∞) (hf : ∀ i, StronglyMeasurable (f i))
     (hfu : UniformIntegrable f p μ) {ε : ℝ} (hε : 0 < ε) :
@@ -995,7 +1078,9 @@ theorem UniformIntegrable.spec' (hp : p ≠ 0) (hp' : p ≠ ∞) (hf : ∀ i, St
     exact lt_two_mul_self (lt_max_of_lt_right one_pos)
   exact ⟨C, fun i => hδ i _ (measurableSet_le measurable_const (hf i).nnnorm.Measurable) (hC i)⟩
 #align measure_theory.uniform_integrable.spec' MeasureTheory.UniformIntegrable.spec'
+-/
 
+#print MeasureTheory.UniformIntegrable.spec /-
 theorem UniformIntegrable.spec (hp : p ≠ 0) (hp' : p ≠ ∞) (hfu : UniformIntegrable f p μ) {ε : ℝ}
     (hε : 0 < ε) :
     ∃ C : ℝ≥0, ∀ i, snorm ({x | C ≤ ‖f i x‖₊}.indicator (f i)) p μ ≤ ENNReal.ofReal ε :=
@@ -1012,7 +1097,9 @@ theorem UniformIntegrable.spec (hp : p ≠ 0) (hp' : p ≠ ∞) (hfu : UniformIn
   · rw [indicator_of_not_mem hfx, indicator_of_not_mem]
     rwa [mem_set_of, hx] at hfx 
 #align measure_theory.uniform_integrable.spec MeasureTheory.UniformIntegrable.spec
+-/
 
+#print MeasureTheory.uniformIntegrable_iff /-
 /-- The definition of uniform integrable in mathlib is equivalent to the definition commonly
 found in literature. -/
 theorem uniformIntegrable_iff [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞) :
@@ -1024,7 +1111,9 @@ theorem uniformIntegrable_iff [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ 
   ⟨fun h => ⟨h.1, fun ε => h.spec (lt_of_lt_of_le zero_lt_one hp).Ne.symm hp'⟩, fun h =>
     uniformIntegrable_of hp hp' h.1 h.2⟩
 #align measure_theory.uniform_integrable_iff MeasureTheory.uniformIntegrable_iff
+-/
 
+#print MeasureTheory.uniformIntegrable_average /-
 /-- The averaging of a uniformly integrable sequence is also uniformly integrable. -/
 theorem uniformIntegrable_average (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf : UniformIntegrable f p μ) :
     UniformIntegrable (fun n => (∑ i in Finset.range n, f i) / n) p μ :=
@@ -1079,6 +1168,7 @@ theorem uniformIntegrable_average (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf :
       · exact le_rfl
       all_goals simpa only [Ne.def, Nat.cast_eq_zero]
 #align measure_theory.uniform_integrable_average MeasureTheory.uniformIntegrable_average
+-/
 
 end UniformIntegrable
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -186,8 +186,7 @@ variable {f : α → β}
 /-- This lemma is weaker than `measure_theory.mem_ℒp.integral_indicator_norm_ge_nonneg_le`
 as the latter provides `0 ≤ M` and does not require the measurability of `f`. -/
 theorem Memℒp.integral_indicator_norm_ge_le (hf : Memℒp f 1 μ) (hmeas : StronglyMeasurable f)
-    {ε : ℝ} (hε : 0 < ε) :
-    ∃ M : ℝ, (∫⁻ x, ‖{x | M ≤ ‖f x‖₊}.indicator f x‖₊ ∂μ) ≤ ENNReal.ofReal ε :=
+    {ε : ℝ} (hε : 0 < ε) : ∃ M : ℝ, ∫⁻ x, ‖{x | M ≤ ‖f x‖₊}.indicator f x‖₊ ∂μ ≤ ENNReal.ofReal ε :=
   by
   have htendsto :
     ∀ᵐ x ∂μ, tendsto (fun M : ℕ => {x | (M : ℝ) ≤ ‖f x‖₊}.indicator f x) at_top (𝓝 0) :=
@@ -227,13 +226,13 @@ theorem Memℒp.integral_indicator_norm_ge_le (hf : Memℒp f 1 μ) (hmeas : Str
 which does not require measurability. -/
 theorem Memℒp.integral_indicator_norm_ge_nonneg_le_of_meas (hf : Memℒp f 1 μ)
     (hmeas : StronglyMeasurable f) {ε : ℝ} (hε : 0 < ε) :
-    ∃ M : ℝ, 0 ≤ M ∧ (∫⁻ x, ‖{x | M ≤ ‖f x‖₊}.indicator f x‖₊ ∂μ) ≤ ENNReal.ofReal ε :=
+    ∃ M : ℝ, 0 ≤ M ∧ ∫⁻ x, ‖{x | M ≤ ‖f x‖₊}.indicator f x‖₊ ∂μ ≤ ENNReal.ofReal ε :=
   let ⟨M, hM⟩ := hf.integral_indicator_norm_ge_le μ hmeas hε
   ⟨max M 0, le_max_right _ _, by simpa⟩
 #align measure_theory.mem_ℒp.integral_indicator_norm_ge_nonneg_le_of_meas MeasureTheory.Memℒp.integral_indicator_norm_ge_nonneg_le_of_meas
 
 theorem Memℒp.integral_indicator_norm_ge_nonneg_le (hf : Memℒp f 1 μ) {ε : ℝ} (hε : 0 < ε) :
-    ∃ M : ℝ, 0 ≤ M ∧ (∫⁻ x, ‖{x | M ≤ ‖f x‖₊}.indicator f x‖₊ ∂μ) ≤ ENNReal.ofReal ε :=
+    ∃ M : ℝ, 0 ≤ M ∧ ∫⁻ x, ‖{x | M ≤ ‖f x‖₊}.indicator f x‖₊ ∂μ ≤ ENNReal.ofReal ε :=
   by
   have hf_mk : mem_ℒp (hf.1.mk f) 1 μ := (mem_ℒp_congr_ae hf.1.ae_eq_mk).mp hf
   obtain ⟨M, hM_pos, hfM⟩ :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -775,7 +775,6 @@ theorem unifIntegrable_of' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → 
       by
       rw [← ENNReal.ofReal_add (half_pos hε).le (half_pos hε).le, add_halves]
       exact le_rfl
-    
 #align measure_theory.unif_integrable_of' MeasureTheory.unifIntegrable_of'
 
 theorem unifIntegrable_of (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β}
@@ -928,7 +927,6 @@ theorem uniformIntegrable_of' [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ 
               (ENNReal.rpow_ne_top_of_nonneg (inv_nonneg.2 ENNReal.toReal_nonneg)
                 (measure_lt_top _ _).Ne),
             ENNReal.one_ne_top⟩
-    
 #align measure_theory.uniform_integrable_of' MeasureTheory.uniformIntegrable_of'
 
 /-- A sequene of functions `(fₙ)` is uniformly integrable in the probability sense if for all
@@ -985,7 +983,6 @@ theorem UniformIntegrable.spec' (hp : p ≠ 0) (hp' : p ≠ ∞) (hf : ∀ i, St
               (eventually_of_forall fun x hx => _)
           rwa [nnnorm_indicator_eq_indicator_nnnorm, indicator_of_mem hx]
         _ ≤ snorm (f (ℐ C)) p μ := snorm_indicator_le _
-        
     specialize this (2 * max M 1 * δ⁻¹ ^ (1 / p.to_real))
     rw [ENNReal.coe_rpow_of_nonneg _ (one_div_nonneg.2 ENNReal.toReal_nonneg), ← ENNReal.coe_smul,
       smul_eq_mul, mul_assoc, NNReal.inv_rpow,

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
 
 ! This file was ported from Lean 3 source module measure_theory.function.uniform_integrable
-! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
+! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.MeasureTheory.Function.L1Space
 /-!
 # Uniform integrability
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains the definitions for uniform integrability (both in the measure theory sense
 as well as the probability theory sense). This file also contains the Vitali convergence theorem
 which estabishes a relation between uniform integrability, convergence in measure and
@@ -58,6 +61,7 @@ open Set Filter TopologicalSpace
 
 variable {α β ι : Type _} {m : MeasurableSpace α} {μ : Measure α} [NormedAddCommGroup β]
 
+#print MeasureTheory.UnifIntegrable /-
 /-- Uniform integrability in the measure theory sense.
 
 A sequence of functions `f` is said to be uniformly integrable if for all `ε > 0`, there exists
@@ -71,19 +75,22 @@ def UnifIntegrable {m : MeasurableSpace α} (f : ι → α → β) (p : ℝ≥0
       ∀ i s,
         MeasurableSet s → μ s ≤ ENNReal.ofReal δ → snorm (s.indicator (f i)) p μ ≤ ENNReal.ofReal ε
 #align measure_theory.unif_integrable MeasureTheory.UnifIntegrable
+-/
 
+#print MeasureTheory.UniformIntegrable /-
 /-- In probability theory, a family of measurable functions is uniformly integrable if it is
 uniformly integrable in the measure theory sense and is uniformly bounded. -/
 def UniformIntegrable {m : MeasurableSpace α} (f : ι → α → β) (p : ℝ≥0∞) (μ : Measure α) : Prop :=
   (∀ i, AEStronglyMeasurable (f i) μ) ∧ UnifIntegrable f p μ ∧ ∃ C : ℝ≥0, ∀ i, snorm (f i) p μ ≤ C
 #align measure_theory.uniform_integrable MeasureTheory.UniformIntegrable
+-/
 
 namespace UniformIntegrable
 
-protected theorem aEStronglyMeasurable {f : ι → α → β} {p : ℝ≥0∞} (hf : UniformIntegrable f p μ)
+protected theorem aeStronglyMeasurable {f : ι → α → β} {p : ℝ≥0∞} (hf : UniformIntegrable f p μ)
     (i : ι) : AEStronglyMeasurable (f i) μ :=
   hf.1 i
-#align measure_theory.uniform_integrable.ae_strongly_measurable MeasureTheory.UniformIntegrable.aEStronglyMeasurable
+#align measure_theory.uniform_integrable.ae_strongly_measurable MeasureTheory.UniformIntegrable.aeStronglyMeasurable
 
 protected theorem unifIntegrable {f : ι → α → β} {p : ℝ≥0∞} (hf : UniformIntegrable f p μ) :
     UnifIntegrable f p μ :=
@@ -143,7 +150,7 @@ protected theorem ae_eq (hf : UnifIntegrable f p μ) (hfg : ∀ n, f n =ᵐ[μ]
   intro ε hε
   obtain ⟨δ, hδ_pos, hfδ⟩ := hf hε
   refine' ⟨δ, hδ_pos, fun n s hs hμs => (le_of_eq <| snorm_congr_ae _).trans (hfδ n s hs hμs)⟩
-  filter_upwards [hfg n]with x hx
+  filter_upwards [hfg n] with x hx
   simp_rw [indicator_apply, hx]
 #align measure_theory.unif_integrable.ae_eq MeasureTheory.UnifIntegrable.ae_eq
 
@@ -159,7 +166,7 @@ theorem unifIntegrable_congr_ae {p : ℝ≥0∞} {f g : ι → α → β} (hfg :
 #align measure_theory.unif_integrable_congr_ae MeasureTheory.unifIntegrable_congr_ae
 
 theorem tendsto_indicator_ge (f : α → β) (x : α) :
-    Tendsto (fun M : ℕ => { x | (M : ℝ) ≤ ‖f x‖₊ }.indicator f x) atTop (𝓝 0) :=
+    Tendsto (fun M : ℕ => {x | (M : ℝ) ≤ ‖f x‖₊}.indicator f x) atTop (𝓝 0) :=
   by
   refine' @tendsto_atTop_of_eventually_const _ _ _ _ _ _ _ (Nat.ceil (‖f x‖₊ : ℝ) + 1) fun n hn => _
   rw [indicator_of_not_mem]
@@ -180,12 +187,12 @@ variable {f : α → β}
 as the latter provides `0 ≤ M` and does not require the measurability of `f`. -/
 theorem Memℒp.integral_indicator_norm_ge_le (hf : Memℒp f 1 μ) (hmeas : StronglyMeasurable f)
     {ε : ℝ} (hε : 0 < ε) :
-    ∃ M : ℝ, (∫⁻ x, ‖{ x | M ≤ ‖f x‖₊ }.indicator f x‖₊ ∂μ) ≤ ENNReal.ofReal ε :=
+    ∃ M : ℝ, (∫⁻ x, ‖{x | M ≤ ‖f x‖₊}.indicator f x‖₊ ∂μ) ≤ ENNReal.ofReal ε :=
   by
   have htendsto :
-    ∀ᵐ x ∂μ, tendsto (fun M : ℕ => { x | (M : ℝ) ≤ ‖f x‖₊ }.indicator f x) at_top (𝓝 0) :=
+    ∀ᵐ x ∂μ, tendsto (fun M : ℕ => {x | (M : ℝ) ≤ ‖f x‖₊}.indicator f x) at_top (𝓝 0) :=
     univ_mem' (id fun x => tendsto_indicator_ge f x)
-  have hmeas : ∀ M : ℕ, ae_strongly_measurable ({ x | (M : ℝ) ≤ ‖f x‖₊ }.indicator f) μ :=
+  have hmeas : ∀ M : ℕ, ae_strongly_measurable ({x | (M : ℝ) ≤ ‖f x‖₊}.indicator f) μ :=
     by
     intro M
     apply hf.1.indicator
@@ -220,34 +227,34 @@ theorem Memℒp.integral_indicator_norm_ge_le (hf : Memℒp f 1 μ) (hmeas : Str
 which does not require measurability. -/
 theorem Memℒp.integral_indicator_norm_ge_nonneg_le_of_meas (hf : Memℒp f 1 μ)
     (hmeas : StronglyMeasurable f) {ε : ℝ} (hε : 0 < ε) :
-    ∃ M : ℝ, 0 ≤ M ∧ (∫⁻ x, ‖{ x | M ≤ ‖f x‖₊ }.indicator f x‖₊ ∂μ) ≤ ENNReal.ofReal ε :=
+    ∃ M : ℝ, 0 ≤ M ∧ (∫⁻ x, ‖{x | M ≤ ‖f x‖₊}.indicator f x‖₊ ∂μ) ≤ ENNReal.ofReal ε :=
   let ⟨M, hM⟩ := hf.integral_indicator_norm_ge_le μ hmeas hε
   ⟨max M 0, le_max_right _ _, by simpa⟩
 #align measure_theory.mem_ℒp.integral_indicator_norm_ge_nonneg_le_of_meas MeasureTheory.Memℒp.integral_indicator_norm_ge_nonneg_le_of_meas
 
 theorem Memℒp.integral_indicator_norm_ge_nonneg_le (hf : Memℒp f 1 μ) {ε : ℝ} (hε : 0 < ε) :
-    ∃ M : ℝ, 0 ≤ M ∧ (∫⁻ x, ‖{ x | M ≤ ‖f x‖₊ }.indicator f x‖₊ ∂μ) ≤ ENNReal.ofReal ε :=
+    ∃ M : ℝ, 0 ≤ M ∧ (∫⁻ x, ‖{x | M ≤ ‖f x‖₊}.indicator f x‖₊ ∂μ) ≤ ENNReal.ofReal ε :=
   by
   have hf_mk : mem_ℒp (hf.1.mk f) 1 μ := (mem_ℒp_congr_ae hf.1.ae_eq_mk).mp hf
   obtain ⟨M, hM_pos, hfM⟩ :=
     hf_mk.integral_indicator_norm_ge_nonneg_le_of_meas μ hf.1.stronglyMeasurable_mk hε
   refine' ⟨M, hM_pos, (le_of_eq _).trans hfM⟩
   refine' lintegral_congr_ae _
-  filter_upwards [hf.1.ae_eq_mk]with x hx
+  filter_upwards [hf.1.ae_eq_mk] with x hx
   simp only [indicator_apply, coe_nnnorm, mem_set_of_eq, ENNReal.coe_eq_coe, hx.symm]
 #align measure_theory.mem_ℒp.integral_indicator_norm_ge_nonneg_le MeasureTheory.Memℒp.integral_indicator_norm_ge_nonneg_le
 
 theorem Memℒp.snormEssSup_indicator_norm_ge_eq_zero (hf : Memℒp f ∞ μ)
-    (hmeas : StronglyMeasurable f) : ∃ M : ℝ, snormEssSup ({ x | M ≤ ‖f x‖₊ }.indicator f) μ = 0 :=
+    (hmeas : StronglyMeasurable f) : ∃ M : ℝ, snormEssSup ({x | M ≤ ‖f x‖₊}.indicator f) μ = 0 :=
   by
   have hbdd : snorm_ess_sup f μ < ∞ := hf.snorm_lt_top
   refine' ⟨(snorm f ∞ μ + 1).toReal, _⟩
   rw [snorm_ess_sup_indicator_eq_snorm_ess_sup_restrict]
-  have : μ.restrict { x : α | (snorm f ⊤ μ + 1).toReal ≤ ‖f x‖₊ } = 0 :=
+  have : μ.restrict {x : α | (snorm f ⊤ μ + 1).toReal ≤ ‖f x‖₊} = 0 :=
     by
     simp only [coe_nnnorm, snorm_exponent_top, measure.restrict_eq_zero]
     have :
-      { x : α | (snorm_ess_sup f μ + 1).toReal ≤ ‖f x‖ } ⊆ { x : α | snorm_ess_sup f μ < ‖f x‖₊ } :=
+      {x : α | (snorm_ess_sup f μ + 1).toReal ≤ ‖f x‖} ⊆ {x : α | snorm_ess_sup f μ < ‖f x‖₊} :=
       by
       intro x hx
       rw [mem_set_of_eq, ← ENNReal.toReal_lt_toReal hbdd.ne ennreal.coe_lt_top.ne,
@@ -268,7 +275,7 @@ theorem Memℒp.snormEssSup_indicator_norm_ge_eq_zero (hf : Memℒp f ∞ μ)
 /- This lemma is slightly weaker than `measure_theory.mem_ℒp.snorm_indicator_norm_ge_pos_le` as the
 latter provides `0 < M`. -/
 theorem Memℒp.snorm_indicator_norm_ge_le (hf : Memℒp f p μ) (hmeas : StronglyMeasurable f) {ε : ℝ}
-    (hε : 0 < ε) : ∃ M : ℝ, snorm ({ x | M ≤ ‖f x‖₊ }.indicator f) p μ ≤ ENNReal.ofReal ε :=
+    (hε : 0 < ε) : ∃ M : ℝ, snorm ({x | M ≤ ‖f x‖₊}.indicator f) p μ ≤ ENNReal.ofReal ε :=
   by
   by_cases hp_ne_zero : p = 0
   · refine' ⟨1, hp_ne_zero.symm ▸ _⟩
@@ -297,7 +304,7 @@ theorem Memℒp.snorm_indicator_norm_ge_le (hf : Memℒp f p μ) (hmeas : Strong
         (one_div_pos.2 <| ENNReal.toReal_pos hp_ne_zero hp_ne_top),
       ← Real.rpow_mul (norm_nonneg _),
       mul_one_div_cancel (ENNReal.toReal_pos hp_ne_zero hp_ne_top).Ne.symm, Real.rpow_one]
-  by_cases hx : x ∈ { x : α | M ^ (1 / p.to_real) ≤ ‖f x‖₊ }
+  by_cases hx : x ∈ {x : α | M ^ (1 / p.to_real) ≤ ‖f x‖₊}
   · rw [Set.indicator_of_mem hx, Set.indicator_of_mem, Real.nnnorm_of_nonneg]; rfl
     change _ ≤ _
     rwa [← hiff]
@@ -310,7 +317,7 @@ theorem Memℒp.snorm_indicator_norm_ge_le (hf : Memℒp f p μ) (hmeas : Strong
 /-- This lemma implies that a single function is uniformly integrable (in the probability sense). -/
 theorem Memℒp.snorm_indicator_norm_ge_pos_le (hf : Memℒp f p μ) (hmeas : StronglyMeasurable f)
     {ε : ℝ} (hε : 0 < ε) :
-    ∃ M : ℝ, 0 < M ∧ snorm ({ x | M ≤ ‖f x‖₊ }.indicator f) p μ ≤ ENNReal.ofReal ε :=
+    ∃ M : ℝ, 0 < M ∧ snorm ({x | M ≤ ‖f x‖₊}.indicator f) p μ ≤ ENNReal.ofReal ε :=
   by
   obtain ⟨M, hM⟩ := hf.snorm_indicator_norm_ge_le μ hmeas hε
   refine'
@@ -373,9 +380,9 @@ theorem Memℒp.snorm_indicator_le' (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) (hf
   by
   obtain ⟨M, hMpos, hM⟩ := hf.snorm_indicator_norm_ge_pos_le μ hmeas hε
   obtain ⟨δ, hδpos, hδ⟩ :=
-    @snorm_indicator_le_of_bound _ _ _ μ _ _ ({ x | ‖f x‖ < M }.indicator f) hp_top _ hε M _
+    @snorm_indicator_le_of_bound _ _ _ μ _ _ ({x | ‖f x‖ < M}.indicator f) hp_top _ hε M _
   · refine' ⟨δ, hδpos, fun s hs hμs => _⟩
-    rw [(_ : f = { x : α | M ≤ ‖f x‖₊ }.indicator f + { x : α | ‖f x‖ < M }.indicator f)]
+    rw [(_ : f = {x : α | M ≤ ‖f x‖₊}.indicator f + {x : α | ‖f x‖ < M}.indicator f)]
     · rw [snorm_indicator_eq_snorm_restrict hs]
       refine' le_trans (snorm_add_le _ _ hp_one) _
       ·
@@ -517,7 +524,7 @@ theorem snorm_sub_le_of_dist_bdd {p : ℝ≥0∞} (hp' : p ≠ ∞) {s : Set α}
 #align measure_theory.snorm_sub_le_of_dist_bdd MeasureTheory.snorm_sub_le_of_dist_bdd
 
 /-- A sequence of uniformly integrable functions which converges μ-a.e. converges in Lp. -/
-theorem tendsto_Lp_of_tendsto_ae_of_meas [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
+theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
     {f : ℕ → α → β} {g : α → β} (hf : ∀ n, StronglyMeasurable (f n)) (hg : StronglyMeasurable g)
     (hg' : Memℒp g p μ) (hui : UnifIntegrable f p μ)
     (hfg : ∀ᵐ x ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))) :
@@ -602,7 +609,7 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [FiniteMeasure μ] (hp : 1 ≤ p) (hp'
 #align measure_theory.tendsto_Lp_of_tendsto_ae_of_meas MeasureTheory.tendsto_Lp_of_tendsto_ae_of_meas
 
 /-- A sequence of uniformly integrable functions which converges μ-a.e. converges in Lp. -/
-theorem tendsto_Lp_of_tendsto_ae [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ℕ → α → β}
+theorem tendsto_Lp_of_tendsto_ae [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ℕ → α → β}
     {g : α → β} (hf : ∀ n, AEStronglyMeasurable (f n) μ) (hg : Memℒp g p μ)
     (hui : UnifIntegrable f p μ) (hfg : ∀ᵐ x ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))) :
     Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0) :=
@@ -618,7 +625,7 @@ theorem tendsto_Lp_of_tendsto_ae [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠
     by
     rw [ae_all_iff]
     exact fun n => (hf n).ae_eq_mk
-  filter_upwards [hfg, h_ae_forall_eq, hg.1.ae_eq_mk]with x hx_tendsto hxf_eq hxg_eq
+  filter_upwards [hfg, h_ae_forall_eq, hg.1.ae_eq_mk] with x hx_tendsto hxf_eq hxg_eq
   rw [← hxg_eq]
   convert hx_tendsto
   ext1 n
@@ -659,7 +666,7 @@ theorem unifIntegrable_of_tendsto_Lp (hp : 1 ≤ p) (hp' : p ≠ ∞) (hf : ∀
 /-- Forward direction of Vitali's convergence theorem: if `f` is a sequence of uniformly integrable
 functions that converge in measure to some function `g` in a finite measure space, then `f`
 converge in Lp to `g`. -/
-theorem tendsto_Lp_of_tendstoInMeasure [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
+theorem tendsto_Lp_of_tendstoInMeasure [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
     (hf : ∀ n, AEStronglyMeasurable (f n) μ) (hg : Memℒp g p μ) (hui : UnifIntegrable f p μ)
     (hfg : TendstoInMeasure μ f atTop g) : Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0) :=
   by
@@ -676,7 +683,7 @@ theorem tendsto_Lp_of_tendstoInMeasure [FiniteMeasure μ] (hp : 1 ≤ p) (hp' :
 
 /-- **Vitali's convergence theorem**: A sequence of functions `f` converges to `g` in Lp if and
 only if it is uniformly integrable and converges to `g` in measure. -/
-theorem tendstoInMeasure_iff_tendsto_Lp [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
+theorem tendstoInMeasure_iff_tendsto_Lp [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
     (hf : ∀ n, Memℒp (f n) p μ) (hg : Memℒp g p μ) :
     TendstoInMeasure μ f atTop g ∧ UnifIntegrable f p μ ↔
       Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0) :=
@@ -693,7 +700,7 @@ theorem unifIntegrable_of' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → 
       ∀ ε : ℝ,
         0 < ε →
           ∃ C : ℝ≥0,
-            0 < C ∧ ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε) :
+            0 < C ∧ ∀ i, snorm ({x | C ≤ ‖f i x‖₊}.indicator (f i)) p μ ≤ ENNReal.ofReal ε) :
     UnifIntegrable f p μ :=
   by
   have hpzero := (lt_of_lt_of_le zero_lt_one hp).Ne.symm
@@ -712,8 +719,8 @@ theorem unifIntegrable_of' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → 
     norm_num
   calc
     snorm (indicator s (f i)) p μ ≤
-        snorm (indicator (s ∩ { x | C ≤ ‖f i x‖₊ }) (f i)) p μ +
-          snorm (indicator (s ∩ { x | ‖f i x‖₊ < C }) (f i)) p μ :=
+        snorm (indicator (s ∩ {x | C ≤ ‖f i x‖₊}) (f i)) p μ +
+          snorm (indicator (s ∩ {x | ‖f i x‖₊ < C}) (f i)) p μ :=
       by
       refine'
         le_trans (Eq.le _)
@@ -728,25 +735,24 @@ theorem unifIntegrable_of' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → 
       congr
       change
         _ = fun x =>
-          (s ∩ { x : α | C ≤ ‖f i x‖₊ }).indicator (f i) x +
-            (s ∩ { x : α | ‖f i x‖₊ < C }).indicator (f i) x
+          (s ∩ {x : α | C ≤ ‖f i x‖₊}).indicator (f i) x +
+            (s ∩ {x : α | ‖f i x‖₊ < C}).indicator (f i) x
       rw [← Set.indicator_union_of_disjoint]
       · congr
         rw [← inter_union_distrib_left,
-          (by ext; simp [le_or_lt] :
-            { x : α | C ≤ ‖f i x‖₊ } ∪ { x : α | ‖f i x‖₊ < C } = Set.univ),
+          (by ext; simp [le_or_lt] : {x : α | C ≤ ‖f i x‖₊} ∪ {x : α | ‖f i x‖₊ < C} = Set.univ),
           inter_univ]
       · refine' (Disjoint.inf_right' _ _).inf_left' _
         rw [disjoint_iff_inf_le]
         rintro x ⟨hx₁ : _ ≤ _, hx₂ : _ < _⟩
         exact False.elim (hx₂.ne (eq_of_le_of_not_lt hx₁ (not_lt.2 hx₂.le)).symm)
-    _ ≤ snorm (indicator { x | C ≤ ‖f i x‖₊ } (f i)) p μ + C * μ s ^ (1 / ENNReal.toReal p) :=
+    _ ≤ snorm (indicator {x | C ≤ ‖f i x‖₊} (f i)) p μ + C * μ s ^ (1 / ENNReal.toReal p) :=
       by
       refine'
         add_le_add (snorm_mono fun x => norm_indicator_le_of_subset (inter_subset_right _ _) _ _) _
       rw [← indicator_indicator]
       rw [snorm_indicator_eq_snorm_restrict]
-      have : ∀ᵐ x ∂μ.restrict s, ‖{ x : α | ‖f i x‖₊ < C }.indicator (f i) x‖ ≤ C :=
+      have : ∀ᵐ x ∂μ.restrict s, ‖{x : α | ‖f i x‖₊ < C}.indicator (f i) x‖ ≤ C :=
         by
         refine' ae_of_all _ _
         simp_rw [norm_indicator_eq_indicator_norm]
@@ -776,20 +782,19 @@ theorem unifIntegrable_of (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β
     (hf : ∀ i, AEStronglyMeasurable (f i) μ)
     (h :
       ∀ ε : ℝ,
-        0 < ε →
-          ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε) :
+        0 < ε → ∃ C : ℝ≥0, ∀ i, snorm ({x | C ≤ ‖f i x‖₊}.indicator (f i)) p μ ≤ ENNReal.ofReal ε) :
     UnifIntegrable f p μ := by
   set g : ι → α → β := fun i => (hf i).some
   refine'
     (unif_integrable_of' μ hp hp' (fun i => (Exists.choose_spec <| hf i).1) fun ε hε => _).ae_eq
       fun i => (Exists.choose_spec <| hf i).2.symm
   obtain ⟨C, hC⟩ := h ε hε
-  have hCg : ∀ i, snorm ({ x | C ≤ ‖g i x‖₊ }.indicator (g i)) p μ ≤ ENNReal.ofReal ε :=
+  have hCg : ∀ i, snorm ({x | C ≤ ‖g i x‖₊}.indicator (g i)) p μ ≤ ENNReal.ofReal ε :=
     by
     intro i
     refine' le_trans (le_of_eq <| snorm_congr_ae _) (hC i)
-    filter_upwards [(Exists.choose_spec <| hf i).2]with x hx
-    by_cases hfx : x ∈ { x | C ≤ ‖f i x‖₊ }
+    filter_upwards [(Exists.choose_spec <| hf i).2] with x hx
+    by_cases hfx : x ∈ {x | C ≤ ‖f i x‖₊}
     · rw [indicator_of_mem hfx, indicator_of_mem, hx]
       rwa [mem_set_of, hx] at hfx 
     · rw [indicator_of_not_mem hfx, indicator_of_not_mem]
@@ -873,12 +878,11 @@ theorem uniformIntegrable_const {g : α → β} (hp : 1 ≤ p) (hp_ne_top : p 
 
 /-- This lemma is superceded by `uniform_integrable_of` which only requires
 `ae_strongly_measurable`. -/
-theorem uniformIntegrable_of' [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
+theorem uniformIntegrable_of' [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
     (hf : ∀ i, StronglyMeasurable (f i))
     (h :
       ∀ ε : ℝ,
-        0 < ε →
-          ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε) :
+        0 < ε → ∃ C : ℝ≥0, ∀ i, snorm ({x | C ≤ ‖f i x‖₊}.indicator (f i)) p μ ≤ ENNReal.ofReal ε) :
     UniformIntegrable f p μ :=
   by
   refine'
@@ -888,8 +892,8 @@ theorem uniformIntegrable_of' [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞
   refine' ⟨(C * μ univ ^ p.to_real⁻¹ + 1 : ℝ≥0∞).toNNReal, fun i => _⟩
   calc
     snorm (f i) p μ ≤
-        snorm ({ x : α | ‖f i x‖₊ < C }.indicator (f i)) p μ +
-          snorm ({ x : α | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ :=
+        snorm ({x : α | ‖f i x‖₊ < C}.indicator (f i)) p μ +
+          snorm ({x : α | C ≤ ‖f i x‖₊}.indicator (f i)) p μ :=
       by
       refine'
         le_trans (snorm_mono fun x => _)
@@ -907,7 +911,7 @@ theorem uniformIntegrable_of' [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞
           simpa using hx
     _ ≤ C * μ univ ^ p.to_real⁻¹ + 1 :=
       by
-      have : ∀ᵐ x ∂μ, ‖{ x : α | ‖f i x‖₊ < C }.indicator (f i) x‖₊ ≤ C :=
+      have : ∀ᵐ x ∂μ, ‖{x : α | ‖f i x‖₊ < C}.indicator (f i) x‖₊ ≤ C :=
         by
         refine' eventually_of_forall _
         simp_rw [nnnorm_indicator_eq_indicator_nnnorm]
@@ -929,12 +933,11 @@ theorem uniformIntegrable_of' [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞
 
 /-- A sequene of functions `(fₙ)` is uniformly integrable in the probability sense if for all
 `ε > 0`, there exists some `C` such that `∫ x in {|fₙ| ≥ C}, fₙ x ∂μ ≤ ε` for all `n`. -/
-theorem uniformIntegrable_of [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
+theorem uniformIntegrable_of [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
     (hf : ∀ i, AEStronglyMeasurable (f i) μ)
     (h :
       ∀ ε : ℝ,
-        0 < ε →
-          ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε) :
+        0 < ε → ∃ C : ℝ≥0, ∀ i, snorm ({x | C ≤ ‖f i x‖₊}.indicator (f i)) p μ ≤ ENNReal.ofReal ε) :
     UniformIntegrable f p μ :=
   by
   set g : ι → α → β := fun i => (hf i).some
@@ -943,8 +946,8 @@ theorem uniformIntegrable_of [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
   refine' (uniform_integrable_of' hp hp' hgmeas fun ε hε => _).ae_eq hgeq
   obtain ⟨C, hC⟩ := h ε hε
   refine' ⟨C, fun i => le_trans (le_of_eq <| snorm_congr_ae _) (hC i)⟩
-  filter_upwards [(Exists.choose_spec <| hf i).2]with x hx
-  by_cases hfx : x ∈ { x | C ≤ ‖f i x‖₊ }
+  filter_upwards [(Exists.choose_spec <| hf i).2] with x hx
+  by_cases hfx : x ∈ {x | C ≤ ‖f i x‖₊}
   · rw [indicator_of_mem hfx, indicator_of_mem, hx]
     rwa [mem_set_of, hx] at hfx 
   · rw [indicator_of_not_mem hfx, indicator_of_not_mem]
@@ -954,27 +957,27 @@ theorem uniformIntegrable_of [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
 /-- This lemma is superceded by `uniform_integrable.spec` which does not require measurability. -/
 theorem UniformIntegrable.spec' (hp : p ≠ 0) (hp' : p ≠ ∞) (hf : ∀ i, StronglyMeasurable (f i))
     (hfu : UniformIntegrable f p μ) {ε : ℝ} (hε : 0 < ε) :
-    ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε :=
+    ∃ C : ℝ≥0, ∀ i, snorm ({x | C ≤ ‖f i x‖₊}.indicator (f i)) p μ ≤ ENNReal.ofReal ε :=
   by
   obtain ⟨-, hfu, M, hM⟩ := hfu
   obtain ⟨δ, hδpos, hδ⟩ := hfu hε
-  obtain ⟨C, hC⟩ : ∃ C : ℝ≥0, ∀ i, μ { x | C ≤ ‖f i x‖₊ } ≤ ENNReal.ofReal δ :=
+  obtain ⟨C, hC⟩ : ∃ C : ℝ≥0, ∀ i, μ {x | C ≤ ‖f i x‖₊} ≤ ENNReal.ofReal δ :=
     by
-    by_contra hcon; push_neg  at hcon 
+    by_contra hcon; push_neg at hcon 
     choose ℐ hℐ using hcon
     lift δ to ℝ≥0 using hδpos.le
     have : ∀ C : ℝ≥0, C • (δ : ℝ≥0∞) ^ (1 / p.to_real) ≤ snorm (f (ℐ C)) p μ :=
       by
       intro C
       calc
-        C • (δ : ℝ≥0∞) ^ (1 / p.to_real) ≤ C • μ { x | C ≤ ‖f (ℐ C) x‖₊ } ^ (1 / p.to_real) :=
+        C • (δ : ℝ≥0∞) ^ (1 / p.to_real) ≤ C • μ {x | C ≤ ‖f (ℐ C) x‖₊} ^ (1 / p.to_real) :=
           by
           rw [ENNReal.smul_def, ENNReal.smul_def, smul_eq_mul, smul_eq_mul]
           simp_rw [ENNReal.ofReal_coe_nnreal] at hℐ 
           refine'
             mul_le_mul' le_rfl
               (ENNReal.rpow_le_rpow (hℐ C).le (one_div_nonneg.2 ENNReal.toReal_nonneg))
-        _ ≤ snorm ({ x | C ≤ ‖f (ℐ C) x‖₊ }.indicator (f (ℐ C))) p μ :=
+        _ ≤ snorm ({x | C ≤ ‖f (ℐ C) x‖₊}.indicator (f (ℐ C))) p μ :=
           by
           refine'
             snorm_indicator_ge_of_bdd_below hp hp' _
@@ -999,15 +1002,15 @@ theorem UniformIntegrable.spec' (hp : p ≠ 0) (hp' : p ≠ ∞) (hf : ∀ i, St
 
 theorem UniformIntegrable.spec (hp : p ≠ 0) (hp' : p ≠ ∞) (hfu : UniformIntegrable f p μ) {ε : ℝ}
     (hε : 0 < ε) :
-    ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε :=
+    ∃ C : ℝ≥0, ∀ i, snorm ({x | C ≤ ‖f i x‖₊}.indicator (f i)) p μ ≤ ENNReal.ofReal ε :=
   by
   set g : ι → α → β := fun i => (hfu.1 i).some
   have hgmeas : ∀ i, strongly_measurable (g i) := fun i => (Exists.choose_spec <| hfu.1 i).1
   have hgunif : uniform_integrable g p μ := hfu.ae_eq fun i => (Exists.choose_spec <| hfu.1 i).2
   obtain ⟨C, hC⟩ := hgunif.spec' hp hp' hgmeas hε
   refine' ⟨C, fun i => le_trans (le_of_eq <| snorm_congr_ae _) (hC i)⟩
-  filter_upwards [(Exists.choose_spec <| hfu.1 i).2]with x hx
-  by_cases hfx : x ∈ { x | C ≤ ‖f i x‖₊ }
+  filter_upwards [(Exists.choose_spec <| hfu.1 i).2] with x hx
+  by_cases hfx : x ∈ {x | C ≤ ‖f i x‖₊}
   · rw [indicator_of_mem hfx, indicator_of_mem, hx]
     rwa [mem_set_of, hx] at hfx 
   · rw [indicator_of_not_mem hfx, indicator_of_not_mem]
@@ -1016,12 +1019,12 @@ theorem UniformIntegrable.spec (hp : p ≠ 0) (hp' : p ≠ ∞) (hfu : UniformIn
 
 /-- The definition of uniform integrable in mathlib is equivalent to the definition commonly
 found in literature. -/
-theorem uniformIntegrable_iff [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞) :
+theorem uniformIntegrable_iff [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞) :
     UniformIntegrable f p μ ↔
       (∀ i, AEStronglyMeasurable (f i) μ) ∧
         ∀ ε : ℝ,
           0 < ε →
-            ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε :=
+            ∃ C : ℝ≥0, ∀ i, snorm ({x | C ≤ ‖f i x‖₊}.indicator (f i)) p μ ≤ ENNReal.ofReal ε :=
   ⟨fun h => ⟨h.1, fun ε => h.spec (lt_of_lt_of_le zero_lt_one hp).Ne.symm hp'⟩, fun h =>
     uniformIntegrable_of hp hp' h.1 h.2⟩
 #align measure_theory.uniform_integrable_iff MeasureTheory.uniformIntegrable_iff

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -67,7 +67,7 @@ restricted on `s` is less than `ε`.
 Uniform integrablility is also known as uniformly absolutely continuous integrals. -/
 def UnifIntegrable {m : MeasurableSpace α} (f : ι → α → β) (p : ℝ≥0∞) (μ : Measure α) : Prop :=
   ∀ ⦃ε : ℝ⦄ (hε : 0 < ε),
-    ∃ (δ : ℝ)(hδ : 0 < δ),
+    ∃ (δ : ℝ) (hδ : 0 < δ),
       ∀ i s,
         MeasurableSet s → μ s ≤ ENNReal.ofReal δ → snorm (s.indicator (f i)) p μ ≤ ENNReal.ofReal ε
 #align measure_theory.unif_integrable MeasureTheory.UnifIntegrable
@@ -167,7 +167,7 @@ theorem tendsto_indicator_ge (f : α → β) (x : α) :
   refine' lt_of_le_of_lt (Nat.le_ceil _) _
   refine' lt_of_lt_of_le (lt_add_one _) _
   norm_cast
-  rwa [ge_iff_le, coe_nnnorm] at hn
+  rwa [ge_iff_le, coe_nnnorm] at hn 
 #align measure_theory.tendsto_indicator_ge MeasureTheory.tendsto_indicator_ge
 
 variable (μ) {p : ℝ≥0∞}
@@ -194,13 +194,13 @@ theorem Memℒp.integral_indicator_norm_ge_le (hf : Memℒp f 1 μ) (hmeas : Str
         hmeas.nnnorm.measurable.coe_nnreal_real.strongly_measurable
   have hbound : has_finite_integral (fun x => ‖f x‖) μ :=
     by
-    rw [mem_ℒp_one_iff_integrable] at hf
+    rw [mem_ℒp_one_iff_integrable] at hf 
     exact hf.norm.2
   have := tendsto_lintegral_norm_of_dominated_convergence hmeas hbound _ htendsto
-  · rw [ENNReal.tendsto_atTop_zero] at this
+  · rw [ENNReal.tendsto_atTop_zero] at this 
     obtain ⟨M, hM⟩ := this (ENNReal.ofReal ε) (ENNReal.ofReal_pos.2 hε)
     simp only [true_and_iff, ge_iff_le, zero_tsub, zero_le, sub_zero, zero_add, coe_nnnorm,
-      mem_Icc] at hM
+      mem_Icc] at hM 
     refine' ⟨M, _⟩
     convert hM M le_rfl
     ext1 x
@@ -259,7 +259,7 @@ theorem Memℒp.snormEssSup_indicator_norm_ge_eq_zero (hf : Memℒp f ∞ μ)
     rw [← nonpos_iff_eq_zero]
     refine' (measure_mono this).trans _
     have hle := coe_nnnorm_ae_le_snorm_ess_sup f μ
-    simp_rw [ae_iff, not_le] at hle
+    simp_rw [ae_iff, not_le] at hle 
     exact nonpos_iff_eq_zero.2 hle
   rw [this, snorm_ess_sup_measure_zero]
   exact measurableSet_le measurable_const hmeas.nnnorm.measurable.subtype_coe
@@ -317,7 +317,7 @@ theorem Memℒp.snorm_indicator_norm_ge_pos_le (hf : Memℒp f p μ) (hmeas : St
     ⟨max M 1, lt_of_lt_of_le zero_lt_one (le_max_right _ _), le_trans (snorm_mono fun x => _) hM⟩
   rw [norm_indicator_eq_indicator_norm, norm_indicator_eq_indicator_norm]
   refine' indicator_le_indicator_of_subset (fun x hx => _) (fun x => norm_nonneg _) x
-  change max _ _ ≤ _ at hx
+  change max _ _ ≤ _ at hx 
   -- removing the `change` breaks the proof!
   exact (max_le_iff.1 hx).1
 #align measure_theory.mem_ℒp.snorm_indicator_norm_ge_pos_le MeasureTheory.Memℒp.snorm_indicator_norm_ge_pos_le
@@ -327,7 +327,7 @@ end
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], [], []]: ./././Mathport/Syntax/Translate/Basic.lean:349:22: unsupported: parse error @ arg 0: next failed, no more args -/
 theorem snorm_indicator_le_of_bound {f : α → β} (hp_top : p ≠ ∞) {ε : ℝ} (hε : 0 < ε) {M : ℝ}
     (hf : ∀ x, ‖f x‖ < M) :
-    ∃ (δ : ℝ)(hδ : 0 < δ),
+    ∃ (δ : ℝ) (hδ : 0 < δ),
       ∀ s,
         MeasurableSet s → μ s ≤ ENNReal.ofReal δ → snorm (s.indicator f) p μ ≤ ENNReal.ofReal ε :=
   by
@@ -338,7 +338,7 @@ theorem snorm_indicator_le_of_bound {f : α → β} (hp_top : p ≠ ∞) {ε : 
     · ext x
       rw [Pi.zero_apply, ← norm_le_zero_iff]
       exact (lt_of_lt_of_le (hf x) hM).le
-  rw [not_le] at hM
+  rw [not_le] at hM 
   refine' ⟨(ε / M) ^ p.to_real, Real.rpow_pos_of_pos (div_pos hε hM) _, fun s hs hμ => _⟩
   by_cases hp : p = 0
   · simp [hp]
@@ -366,7 +366,7 @@ variable {f : α → β}
 /-- Auxiliary lemma for `measure_theory.mem_ℒp.snorm_indicator_le`. -/
 theorem Memℒp.snorm_indicator_le' (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) (hf : Memℒp f p μ)
     (hmeas : StronglyMeasurable f) {ε : ℝ} (hε : 0 < ε) :
-    ∃ (δ : ℝ)(hδ : 0 < δ),
+    ∃ (δ : ℝ) (hδ : 0 < δ),
       ∀ s,
         MeasurableSet s →
           μ s ≤ ENNReal.ofReal δ → snorm (s.indicator f) p μ ≤ 2 * ENNReal.ofReal ε :=
@@ -399,14 +399,14 @@ theorem Memℒp.snorm_indicator_le' (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) (hf
   · intro x
     rw [norm_indicator_eq_indicator_norm, indicator_apply]
     split_ifs
-    exacts[h, hMpos]
+    exacts [h, hMpos]
 #align measure_theory.mem_ℒp.snorm_indicator_le' MeasureTheory.Memℒp.snorm_indicator_le'
 
 /-- This lemma is superceded by `measure_theory.mem_ℒp.snorm_indicator_le` which does not require
 measurability on `f`. -/
 theorem Memℒp.snorm_indicator_le_of_meas (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) (hf : Memℒp f p μ)
     (hmeas : StronglyMeasurable f) {ε : ℝ} (hε : 0 < ε) :
-    ∃ (δ : ℝ)(hδ : 0 < δ),
+    ∃ (δ : ℝ) (hδ : 0 < δ),
       ∀ s,
         MeasurableSet s → μ s ≤ ENNReal.ofReal δ → snorm (s.indicator f) p μ ≤ ENNReal.ofReal ε :=
   by
@@ -419,7 +419,7 @@ theorem Memℒp.snorm_indicator_le_of_meas (hp_one : 1 ≤ p) (hp_top : p ≠ 
 
 theorem Memℒp.snorm_indicator_le (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) (hf : Memℒp f p μ) {ε : ℝ}
     (hε : 0 < ε) :
-    ∃ (δ : ℝ)(hδ : 0 < δ),
+    ∃ (δ : ℝ) (hδ : 0 < δ),
       ∀ s,
         MeasurableSet s → μ s ≤ ENNReal.ofReal δ → snorm (s.indicator f) p μ ≤ ENNReal.ofReal ε :=
   by
@@ -474,8 +474,8 @@ theorem unifIntegrable_fin (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) {n : ℕ} {f
   · rw [(_ : i = n)]
     · exact hδ₂ _ hs (le_trans hμs <| ENNReal.ofReal_le_ofReal <| min_le_right _ _)
     · have hi' := Fin.is_lt i
-      rw [Nat.lt_succ_iff] at hi'
-      rw [not_lt] at hi
+      rw [Nat.lt_succ_iff] at hi' 
+      rw [not_lt] at hi 
       simp [← le_antisymm hi' hi]
 #align measure_theory.unif_integrable_fin MeasureTheory.unifIntegrable_fin
 
@@ -490,7 +490,7 @@ theorem unifIntegrable_finite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞
   obtain ⟨δ, hδpos, hδ⟩ := unif_integrable_fin μ hp_one hp_top hg hε
   refine' ⟨δ, hδpos, fun i s hs hμs => _⟩
   specialize hδ (hn.some i) s hs hμs
-  simp_rw [hgeq, Function.comp_apply, Equiv.symm_apply_apply] at hδ
+  simp_rw [hgeq, Function.comp_apply, Equiv.symm_apply_apply] at hδ 
   assumption
 #align measure_theory.unif_integrable_finite MeasureTheory.unifIntegrable_finite
 
@@ -526,7 +526,7 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [FiniteMeasure μ] (hp : 1 ≤ p) (hp'
   rw [ENNReal.tendsto_atTop_zero]
   intro ε hε
   by_cases ε < ∞; swap
-  · rw [not_lt, top_le_iff] at h
+  · rw [not_lt, top_le_iff] at h 
     exact ⟨0, fun n hn => by simp [h]⟩
   by_cases hμ : μ = 0
   · exact ⟨0, fun n hn => by simp [hμ]⟩
@@ -541,7 +541,7 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [FiniteMeasure μ] (hp : 1 ≤ p) (hp'
   obtain ⟨δ₁, hδ₁, hsnorm₁⟩ := hui hε'
   obtain ⟨δ₂, hδ₂, hsnorm₂⟩ := hg'.snorm_indicator_le μ hp hp' hε'
   obtain ⟨t, htm, ht₁, ht₂⟩ := tendsto_uniformly_on_of_ae_tendsto' hf hg hfg (lt_min hδ₁ hδ₂)
-  rw [Metric.tendstoUniformlyOn_iff] at ht₂
+  rw [Metric.tendstoUniformlyOn_iff] at ht₂ 
   specialize
     ht₂ (ε.to_real / (3 * measure_univ_nnreal μ ^ (1 / p.to_real)))
       (div_pos (ENNReal.toReal_pos (gt_iff_lt.1 hε).Ne.symm h.ne) (mul_pos (by norm_num) hpow))
@@ -596,7 +596,7 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [FiniteMeasure μ] (hp : 1 ≤ p) (hp'
     by
     rw [ENNReal.ofReal_div_of_pos (show (0 : ℝ) < 3 by norm_num), ENNReal.ofReal_toReal h.ne]
     simp
-  rw [this] at hnf hng hlt
+  rw [this] at hnf hng hlt 
   rw [snorm_neg, ← ENNReal.add_thirds ε, ← sub_eq_add_neg]
   exact add_le_add_three hnf hng hlt
 #align measure_theory.tendsto_Lp_of_tendsto_ae_of_meas MeasureTheory.tendsto_Lp_of_tendsto_ae_of_meas
@@ -631,7 +631,7 @@ theorem unifIntegrable_of_tendsto_Lp_zero (hp : 1 ≤ p) (hp' : p ≠ ∞) (hf :
     (hf_tendsto : Tendsto (fun n => snorm (f n) p μ) atTop (𝓝 0)) : UnifIntegrable f p μ :=
   by
   intro ε hε
-  rw [ENNReal.tendsto_atTop_zero] at hf_tendsto
+  rw [ENNReal.tendsto_atTop_zero] at hf_tendsto 
   obtain ⟨N, hN⟩ := hf_tendsto (ENNReal.ofReal ε) (by simpa)
   set F : Fin N → α → β := fun n => f n
   have hF : ∀ n, mem_ℒp (F n) p μ := fun n => hf n
@@ -698,7 +698,7 @@ theorem unifIntegrable_of' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → 
   by
   have hpzero := (lt_of_lt_of_le zero_lt_one hp).Ne.symm
   by_cases hμ : μ Set.univ = 0
-  · rw [measure.measure_univ_eq_zero] at hμ
+  · rw [measure.measure_univ_eq_zero] at hμ 
     exact hμ.symm ▸ unif_integrable_zero_meas
   intro ε hε
   obtain ⟨C, hCpos, hC⟩ := h (ε / 2) (half_pos hε)
@@ -753,7 +753,7 @@ theorem unifIntegrable_of' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → 
         exact indicator_le' (fun x (hx : _ < _) => hx.le) fun _ _ => NNReal.coe_nonneg _
       refine' le_trans (snorm_le_of_ae_bound this) _
       rw [mul_comm, measure.restrict_apply' hs, univ_inter, ENNReal.ofReal_coe_nnreal, one_div]
-      exacts[le_rfl, hs]
+      exacts [le_rfl, hs]
     _ ≤ ENNReal.ofReal (ε / 2) + C * ENNReal.ofReal (ε / (2 * C)) :=
       by
       refine' add_le_add (hC i) (mul_le_mul_left' _ _)
@@ -791,9 +791,9 @@ theorem unifIntegrable_of (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β
     filter_upwards [(Exists.choose_spec <| hf i).2]with x hx
     by_cases hfx : x ∈ { x | C ≤ ‖f i x‖₊ }
     · rw [indicator_of_mem hfx, indicator_of_mem, hx]
-      rwa [mem_set_of, hx] at hfx
+      rwa [mem_set_of, hx] at hfx 
     · rw [indicator_of_not_mem hfx, indicator_of_not_mem]
-      rwa [mem_set_of, hx] at hfx
+      rwa [mem_set_of, hx] at hfx 
   refine' ⟨max C 1, lt_max_of_lt_right one_pos, fun i => le_trans (snorm_mono fun x => _) (hCg i)⟩
   rw [norm_indicator_eq_indicator_norm, norm_indicator_eq_indicator_norm]
   exact
@@ -852,7 +852,7 @@ theorem uniformIntegrable_finite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠
     rw [ENNReal.coe_toNNReal]
     · exact Finset.le_max' _ _ (Finset.mem_image.2 ⟨i, Finset.mem_univ _, rfl⟩)
     · refine' ne_of_lt ((Finset.max'_lt_iff _ _).2 fun y hy => _)
-      rw [Finset.mem_image] at hy
+      rw [Finset.mem_image] at hy 
       obtain ⟨i, -, rfl⟩ := hy
       exact hf i
   · exact ⟨0, fun i => False.elim <| hι <| Nonempty.intro i⟩
@@ -946,9 +946,9 @@ theorem uniformIntegrable_of [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
   filter_upwards [(Exists.choose_spec <| hf i).2]with x hx
   by_cases hfx : x ∈ { x | C ≤ ‖f i x‖₊ }
   · rw [indicator_of_mem hfx, indicator_of_mem, hx]
-    rwa [mem_set_of, hx] at hfx
+    rwa [mem_set_of, hx] at hfx 
   · rw [indicator_of_not_mem hfx, indicator_of_not_mem]
-    rwa [mem_set_of, hx] at hfx
+    rwa [mem_set_of, hx] at hfx 
 #align measure_theory.uniform_integrable_of MeasureTheory.uniformIntegrable_of
 
 /-- This lemma is superceded by `uniform_integrable.spec` which does not require measurability. -/
@@ -960,7 +960,7 @@ theorem UniformIntegrable.spec' (hp : p ≠ 0) (hp' : p ≠ ∞) (hf : ∀ i, St
   obtain ⟨δ, hδpos, hδ⟩ := hfu hε
   obtain ⟨C, hC⟩ : ∃ C : ℝ≥0, ∀ i, μ { x | C ≤ ‖f i x‖₊ } ≤ ENNReal.ofReal δ :=
     by
-    by_contra hcon; push_neg  at hcon
+    by_contra hcon; push_neg  at hcon 
     choose ℐ hℐ using hcon
     lift δ to ℝ≥0 using hδpos.le
     have : ∀ C : ℝ≥0, C • (δ : ℝ≥0∞) ^ (1 / p.to_real) ≤ snorm (f (ℐ C)) p μ :=
@@ -970,7 +970,7 @@ theorem UniformIntegrable.spec' (hp : p ≠ 0) (hp' : p ≠ ∞) (hf : ∀ i, St
         C • (δ : ℝ≥0∞) ^ (1 / p.to_real) ≤ C • μ { x | C ≤ ‖f (ℐ C) x‖₊ } ^ (1 / p.to_real) :=
           by
           rw [ENNReal.smul_def, ENNReal.smul_def, smul_eq_mul, smul_eq_mul]
-          simp_rw [ENNReal.ofReal_coe_nnreal] at hℐ
+          simp_rw [ENNReal.ofReal_coe_nnreal] at hℐ 
           refine'
             mul_le_mul' le_rfl
               (ENNReal.rpow_le_rpow (hℐ C).le (one_div_nonneg.2 ENNReal.toReal_nonneg))
@@ -987,7 +987,7 @@ theorem UniformIntegrable.spec' (hp : p ≠ 0) (hp' : p ≠ ∞) (hf : ∀ i, St
     rw [ENNReal.coe_rpow_of_nonneg _ (one_div_nonneg.2 ENNReal.toReal_nonneg), ← ENNReal.coe_smul,
       smul_eq_mul, mul_assoc, NNReal.inv_rpow,
       inv_mul_cancel (NNReal.rpow_pos (NNReal.coe_pos.1 hδpos)).Ne.symm, mul_one, ENNReal.coe_mul, ←
-      NNReal.inv_rpow] at this
+      NNReal.inv_rpow] at this 
     refine'
       (lt_of_le_of_lt (le_trans (hM <| ℐ <| 2 * max M 1 * δ⁻¹ ^ (1 / p.to_real)) (le_max_left M 1))
             (lt_of_lt_of_le _ this)).Ne
@@ -1009,9 +1009,9 @@ theorem UniformIntegrable.spec (hp : p ≠ 0) (hp' : p ≠ ∞) (hfu : UniformIn
   filter_upwards [(Exists.choose_spec <| hfu.1 i).2]with x hx
   by_cases hfx : x ∈ { x | C ≤ ‖f i x‖₊ }
   · rw [indicator_of_mem hfx, indicator_of_mem, hx]
-    rwa [mem_set_of, hx] at hfx
+    rwa [mem_set_of, hx] at hfx 
   · rw [indicator_of_not_mem hfx, indicator_of_not_mem]
-    rwa [mem_set_of, hx] at hfx
+    rwa [mem_set_of, hx] at hfx 
 #align measure_theory.uniform_integrable.spec MeasureTheory.UniformIntegrable.spec
 
 /-- The definition of uniform integrable in mathlib is equivalent to the definition commonly
@@ -1054,7 +1054,7 @@ theorem uniformIntegrable_average (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf :
     · refine' (ENNReal.mul_le_mul_left hn ENNReal.coe_ne_top).2 _
       conv_rhs => rw [← Finset.card_range n]
       exact Finset.sum_le_card_nsmul _ _ _ fun i hi => hδ₂ _ _ hs hle
-    · simp only [ENNReal.coe_eq_zero, inv_eq_zero, Nat.cast_eq_zero] at hn
+    · simp only [ENNReal.coe_eq_zero, inv_eq_zero, Nat.cast_eq_zero] at hn 
       rw [nsmul_eq_mul, ← mul_assoc, ENNReal.coe_inv, ENNReal.coe_nat,
         ENNReal.inv_mul_cancel _ (ENNReal.nat_ne_top _), one_mul]
       · exact le_rfl
@@ -1074,7 +1074,7 @@ theorem uniformIntegrable_average (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf :
     · refine' (ENNReal.mul_le_mul_left hn ENNReal.coe_ne_top).2 _
       conv_rhs => rw [← Finset.card_range n]
       exact Finset.sum_le_card_nsmul _ _ _ fun i hi => hC i
-    · simp only [ENNReal.coe_eq_zero, inv_eq_zero, Nat.cast_eq_zero] at hn
+    · simp only [ENNReal.coe_eq_zero, inv_eq_zero, Nat.cast_eq_zero] at hn 
       rw [nsmul_eq_mul, ← mul_assoc, ENNReal.coe_inv, ENNReal.coe_nat,
         ENNReal.inv_mul_cancel _ (ENNReal.nat_ne_top _), one_mul]
       · exact le_rfl

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -50,7 +50,7 @@ uniform integrable, uniformly absolutely continuous integral, Vitali convergence
 
 noncomputable section
 
-open Classical MeasureTheory NNReal ENNReal Topology BigOperators
+open scoped Classical MeasureTheory NNReal ENNReal Topology BigOperators
 
 namespace MeasureTheory
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -128,16 +128,13 @@ protected theorem add (hf : UnifIntegrable f p μ) (hg : UnifIntegrable g p μ)
       (hgδ₂ i s hs (hμs.trans (ENNReal.ofReal_le_ofReal (min_le_right _ _))))
 #align measure_theory.unif_integrable.add MeasureTheory.UnifIntegrable.add
 
-protected theorem neg (hf : UnifIntegrable f p μ) : UnifIntegrable (-f) p μ :=
-  by
-  simp_rw [unif_integrable, Pi.neg_apply, indicator_neg', snorm_neg]
-  exact hf
+protected theorem neg (hf : UnifIntegrable f p μ) : UnifIntegrable (-f) p μ := by
+  simp_rw [unif_integrable, Pi.neg_apply, indicator_neg', snorm_neg]; exact hf
 #align measure_theory.unif_integrable.neg MeasureTheory.UnifIntegrable.neg
 
 protected theorem sub (hf : UnifIntegrable f p μ) (hg : UnifIntegrable g p μ) (hp : 1 ≤ p)
     (hf_meas : ∀ i, AEStronglyMeasurable (f i) μ) (hg_meas : ∀ i, AEStronglyMeasurable (g i) μ) :
-    UnifIntegrable (f - g) p μ := by
-  rw [sub_eq_add_neg]
+    UnifIntegrable (f - g) p μ := by rw [sub_eq_add_neg];
   exact hf.add hg.neg hp hf_meas fun i => (hg_meas i).neg
 #align measure_theory.unif_integrable.sub MeasureTheory.UnifIntegrable.sub
 
@@ -301,8 +298,7 @@ theorem Memℒp.snorm_indicator_norm_ge_le (hf : Memℒp f p μ) (hmeas : Strong
       ← Real.rpow_mul (norm_nonneg _),
       mul_one_div_cancel (ENNReal.toReal_pos hp_ne_zero hp_ne_top).Ne.symm, Real.rpow_one]
   by_cases hx : x ∈ { x : α | M ^ (1 / p.to_real) ≤ ‖f x‖₊ }
-  · rw [Set.indicator_of_mem hx, Set.indicator_of_mem, Real.nnnorm_of_nonneg]
-    rfl
+  · rw [Set.indicator_of_mem hx, Set.indicator_of_mem, Real.nnnorm_of_nonneg]; rfl
     change _ ≤ _
     rwa [← hiff]
   · rw [Set.indicator_of_not_mem hx, Set.indicator_of_not_mem]
@@ -474,8 +470,7 @@ theorem unifIntegrable_fin (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) {n : ℕ} {f
   by_cases hi : i.val < n
   · rw [(_ : f i = g ⟨i.val, hi⟩)]
     · exact hδ₁ _ s hs (le_trans hμs <| ENNReal.ofReal_le_ofReal <| min_le_left _ _)
-    · rw [hg]
-      simp
+    · rw [hg]; simp
   · rw [(_ : i = n)]
     · exact hδ₂ _ hs (le_trans hμs <| ENNReal.ofReal_le_ofReal <| min_le_right _ _)
     · have hi' := Fin.is_lt i
@@ -530,8 +525,7 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [FiniteMeasure μ] (hp : 1 ≤ p) (hp'
   by
   rw [ENNReal.tendsto_atTop_zero]
   intro ε hε
-  by_cases ε < ∞
-  swap
+  by_cases ε < ∞; swap
   · rw [not_lt, top_le_iff] at h
     exact ⟨0, fun n hn => by simp [h]⟩
   by_cases hμ : μ = 0
@@ -551,8 +545,7 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [FiniteMeasure μ] (hp : 1 ≤ p) (hp'
   specialize
     ht₂ (ε.to_real / (3 * measure_univ_nnreal μ ^ (1 / p.to_real)))
       (div_pos (ENNReal.toReal_pos (gt_iff_lt.1 hε).Ne.symm h.ne) (mul_pos (by norm_num) hpow))
-  obtain ⟨N, hN⟩ := eventually_at_top.1 ht₂
-  clear ht₂
+  obtain ⟨N, hN⟩ := eventually_at_top.1 ht₂; clear ht₂
   refine' ⟨N, fun n hn => _⟩
   rw [← t.indicator_self_add_compl (f n - g)]
   refine'
@@ -654,10 +647,7 @@ theorem unifIntegrable_of_tendsto_Lp (hp : 1 ≤ p) (hp' : p ≠ ∞) (hf : ∀
     (hg : Memℒp g p μ) (hfg : Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0)) :
     UnifIntegrable f p μ :=
   by
-  have : f = (fun n => g) + fun n => f n - g :=
-    by
-    ext1 n
-    simp
+  have : f = (fun n => g) + fun n => f n - g := by ext1 n; simp
   rw [this]
   refine'
     unif_integrable.add _ _ hp (fun _ => hg.ae_strongly_measurable) fun n =>
@@ -743,9 +733,8 @@ theorem unifIntegrable_of' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → 
       rw [← Set.indicator_union_of_disjoint]
       · congr
         rw [← inter_union_distrib_left,
-          (by
-            ext
-            simp [le_or_lt] : { x : α | C ≤ ‖f i x‖₊ } ∪ { x : α | ‖f i x‖₊ < C } = Set.univ),
+          (by ext; simp [le_or_lt] :
+            { x : α | C ≤ ‖f i x‖₊ } ∪ { x : α | ‖f i x‖₊ < C } = Set.univ),
           inter_univ]
       · refine' (Disjoint.inf_right' _ _).inf_left' _
         rw [disjoint_iff_inf_le]
@@ -971,8 +960,7 @@ theorem UniformIntegrable.spec' (hp : p ≠ 0) (hp' : p ≠ ∞) (hf : ∀ i, St
   obtain ⟨δ, hδpos, hδ⟩ := hfu hε
   obtain ⟨C, hC⟩ : ∃ C : ℝ≥0, ∀ i, μ { x | C ≤ ‖f i x‖₊ } ≤ ENNReal.ofReal δ :=
     by
-    by_contra hcon
-    push_neg  at hcon
+    by_contra hcon; push_neg  at hcon
     choose ℐ hℐ using hcon
     lift δ to ℝ≥0 using hδpos.le
     have : ∀ C : ℝ≥0, C • (δ : ℝ≥0∞) ^ (1 / p.to_real) ≤ snorm (f (ℐ C)) p μ :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -75,15 +75,15 @@ def UnifIntegrable {m : MeasurableSpace α} (f : ι → α → β) (p : ℝ≥0
 /-- In probability theory, a family of measurable functions is uniformly integrable if it is
 uniformly integrable in the measure theory sense and is uniformly bounded. -/
 def UniformIntegrable {m : MeasurableSpace α} (f : ι → α → β) (p : ℝ≥0∞) (μ : Measure α) : Prop :=
-  (∀ i, AeStronglyMeasurable (f i) μ) ∧ UnifIntegrable f p μ ∧ ∃ C : ℝ≥0, ∀ i, snorm (f i) p μ ≤ C
+  (∀ i, AEStronglyMeasurable (f i) μ) ∧ UnifIntegrable f p μ ∧ ∃ C : ℝ≥0, ∀ i, snorm (f i) p μ ≤ C
 #align measure_theory.uniform_integrable MeasureTheory.UniformIntegrable
 
 namespace UniformIntegrable
 
-protected theorem aeStronglyMeasurable {f : ι → α → β} {p : ℝ≥0∞} (hf : UniformIntegrable f p μ)
-    (i : ι) : AeStronglyMeasurable (f i) μ :=
+protected theorem aEStronglyMeasurable {f : ι → α → β} {p : ℝ≥0∞} (hf : UniformIntegrable f p μ)
+    (i : ι) : AEStronglyMeasurable (f i) μ :=
   hf.1 i
-#align measure_theory.uniform_integrable.ae_strongly_measurable MeasureTheory.UniformIntegrable.aeStronglyMeasurable
+#align measure_theory.uniform_integrable.ae_strongly_measurable MeasureTheory.UniformIntegrable.aEStronglyMeasurable
 
 protected theorem unifIntegrable {f : ι → α → β} {p : ℝ≥0∞} (hf : UniformIntegrable f p μ) :
     UnifIntegrable f p μ :=
@@ -111,7 +111,7 @@ namespace UnifIntegrable
 variable {f g : ι → α → β} {p : ℝ≥0∞}
 
 protected theorem add (hf : UnifIntegrable f p μ) (hg : UnifIntegrable g p μ) (hp : 1 ≤ p)
-    (hf_meas : ∀ i, AeStronglyMeasurable (f i) μ) (hg_meas : ∀ i, AeStronglyMeasurable (g i) μ) :
+    (hf_meas : ∀ i, AEStronglyMeasurable (f i) μ) (hg_meas : ∀ i, AEStronglyMeasurable (g i) μ) :
     UnifIntegrable (f + g) p μ := by
   intro ε hε
   have hε2 : 0 < ε / 2 := half_pos hε
@@ -135,7 +135,7 @@ protected theorem neg (hf : UnifIntegrable f p μ) : UnifIntegrable (-f) p μ :=
 #align measure_theory.unif_integrable.neg MeasureTheory.UnifIntegrable.neg
 
 protected theorem sub (hf : UnifIntegrable f p μ) (hg : UnifIntegrable g p μ) (hp : 1 ≤ p)
-    (hf_meas : ∀ i, AeStronglyMeasurable (f i) μ) (hg_meas : ∀ i, AeStronglyMeasurable (g i) μ) :
+    (hf_meas : ∀ i, AEStronglyMeasurable (f i) μ) (hg_meas : ∀ i, AEStronglyMeasurable (g i) μ) :
     UnifIntegrable (f - g) p μ := by
   rw [sub_eq_add_neg]
   exact hf.add hg.neg hp hf_meas fun i => (hg_meas i).neg
@@ -557,15 +557,15 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [FiniteMeasure μ] (hp : 1 ≤ p) (hp'
   rw [← t.indicator_self_add_compl (f n - g)]
   refine'
     le_trans
-      (snorm_add_le (((hf n).sub hg).indicator htm).AeStronglyMeasurable
-        (((hf n).sub hg).indicator htm.compl).AeStronglyMeasurable hp)
+      (snorm_add_le (((hf n).sub hg).indicator htm).AEStronglyMeasurable
+        (((hf n).sub hg).indicator htm.compl).AEStronglyMeasurable hp)
       _
   rw [sub_eq_add_neg, indicator_add' t, indicator_neg']
   refine'
     le_trans
       (add_le_add_right
-        (snorm_add_le ((hf n).indicator htm).AeStronglyMeasurable
-          (hg.indicator htm).neg.AeStronglyMeasurable hp)
+        (snorm_add_le ((hf n).indicator htm).AEStronglyMeasurable
+          (hg.indicator htm).neg.AEStronglyMeasurable hp)
         _)
       _
   have hnf : snorm (t.indicator (f n)) p μ ≤ ENNReal.ofReal (ε.to_real / 3) :=
@@ -610,7 +610,7 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [FiniteMeasure μ] (hp : 1 ≤ p) (hp'
 
 /-- A sequence of uniformly integrable functions which converges μ-a.e. converges in Lp. -/
 theorem tendsto_Lp_of_tendsto_ae [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ℕ → α → β}
-    {g : α → β} (hf : ∀ n, AeStronglyMeasurable (f n) μ) (hg : Memℒp g p μ)
+    {g : α → β} (hf : ∀ n, AEStronglyMeasurable (f n) μ) (hg : Memℒp g p μ)
     (hui : UnifIntegrable f p μ) (hfg : ∀ᵐ x ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))) :
     Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0) :=
   by
@@ -670,7 +670,7 @@ theorem unifIntegrable_of_tendsto_Lp (hp : 1 ≤ p) (hp' : p ≠ ∞) (hf : ∀
 functions that converge in measure to some function `g` in a finite measure space, then `f`
 converge in Lp to `g`. -/
 theorem tendsto_Lp_of_tendstoInMeasure [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
-    (hf : ∀ n, AeStronglyMeasurable (f n) μ) (hg : Memℒp g p μ) (hui : UnifIntegrable f p μ)
+    (hf : ∀ n, AEStronglyMeasurable (f n) μ) (hg : Memℒp g p μ) (hui : UnifIntegrable f p μ)
     (hfg : TendstoInMeasure μ f atTop g) : Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0) :=
   by
   refine' tendsto_of_subseq_tendsto fun ns hns => _
@@ -692,7 +692,7 @@ theorem tendstoInMeasure_iff_tendsto_Lp [FiniteMeasure μ] (hp : 1 ≤ p) (hp' :
       Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0) :=
   ⟨fun h => tendsto_Lp_of_tendstoInMeasure μ hp hp' (fun n => (hf n).1) hg h.2 h.1, fun h =>
     ⟨tendstoInMeasure_of_tendsto_snorm (lt_of_lt_of_le zero_lt_one hp).Ne.symm
-        (fun n => (hf n).AeStronglyMeasurable) hg.AeStronglyMeasurable h,
+        (fun n => (hf n).AEStronglyMeasurable) hg.AEStronglyMeasurable h,
       unifIntegrable_of_tendsto_Lp μ hp hp' hf hg h⟩⟩
 #align measure_theory.tendsto_in_measure_iff_tendsto_Lp MeasureTheory.tendstoInMeasure_iff_tendsto_Lp
 
@@ -717,7 +717,7 @@ theorem unifIntegrable_of' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → 
       Real.rpow_pos_of_pos (div_pos hε (mul_pos two_pos (NNReal.coe_pos.2 hCpos))) _,
       fun i s hs hμs => _⟩
   by_cases hμs' : μ s = 0
-  · rw [(snorm_eq_zero_iff ((hf i).indicator hs).AeStronglyMeasurable hpzero).2
+  · rw [(snorm_eq_zero_iff ((hf i).indicator hs).AEStronglyMeasurable hpzero).2
         (indicator_meas_zero hμs')]
     norm_num
   calc
@@ -784,7 +784,7 @@ theorem unifIntegrable_of' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → 
 #align measure_theory.unif_integrable_of' MeasureTheory.unifIntegrable_of'
 
 theorem unifIntegrable_of (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β}
-    (hf : ∀ i, AeStronglyMeasurable (f i) μ)
+    (hf : ∀ i, AEStronglyMeasurable (f i) μ)
     (h :
       ∀ ε : ℝ,
         0 < ε →
@@ -830,7 +830,7 @@ In this section, we will develope some API for `uniform_integrable` and prove th
 variable {p : ℝ≥0∞} {f : ι → α → β}
 
 theorem uniformIntegrable_zero_meas [MeasurableSpace α] : UniformIntegrable f p (0 : Measure α) :=
-  ⟨fun n => aeStronglyMeasurable_zero_measure _, unifIntegrable_zero_meas, 0, fun i =>
+  ⟨fun n => aestronglyMeasurable_zero_measure _, unifIntegrable_zero_meas, 0, fun i =>
     snorm_measure_zero.le⟩
 #align measure_theory.uniform_integrable_zero_meas MeasureTheory.uniformIntegrable_zero_meas
 
@@ -893,8 +893,8 @@ theorem uniformIntegrable_of' [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞
     UniformIntegrable f p μ :=
   by
   refine'
-    ⟨fun i => (hf i).AeStronglyMeasurable,
-      unif_integrable_of μ hp hp' (fun i => (hf i).AeStronglyMeasurable) h, _⟩
+    ⟨fun i => (hf i).AEStronglyMeasurable,
+      unif_integrable_of μ hp hp' (fun i => (hf i).AEStronglyMeasurable) h, _⟩
   obtain ⟨C, hC⟩ := h 1 one_pos
   refine' ⟨(C * μ univ ^ p.to_real⁻¹ + 1 : ℝ≥0∞).toNNReal, fun i => _⟩
   calc
@@ -941,7 +941,7 @@ theorem uniformIntegrable_of' [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞
 /-- A sequene of functions `(fₙ)` is uniformly integrable in the probability sense if for all
 `ε > 0`, there exists some `C` such that `∫ x in {|fₙ| ≥ C}, fₙ x ∂μ ≤ ε` for all `n`. -/
 theorem uniformIntegrable_of [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
-    (hf : ∀ i, AeStronglyMeasurable (f i) μ)
+    (hf : ∀ i, AEStronglyMeasurable (f i) μ)
     (h :
       ∀ ε : ℝ,
         0 < ε →
@@ -1030,7 +1030,7 @@ theorem UniformIntegrable.spec (hp : p ≠ 0) (hp' : p ≠ ∞) (hfu : UniformIn
 found in literature. -/
 theorem uniformIntegrable_iff [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞) :
     UniformIntegrable f p μ ↔
-      (∀ i, AeStronglyMeasurable (f i) μ) ∧
+      (∀ i, AEStronglyMeasurable (f i) μ) ∧
         ∀ ε : ℝ,
           0 < ε →
             ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε :=
@@ -1046,7 +1046,7 @@ theorem uniformIntegrable_average (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf :
   refine' ⟨fun n => _, fun ε hε => _, _⟩
   · simp_rw [div_eq_mul_inv]
     exact
-      (Finset.aeStronglyMeasurable_sum' _ fun i _ => hf₁ i).mul
+      (Finset.aestronglyMeasurable_sum' _ fun i _ => hf₁ i).mul
         (ae_strongly_measurable_const : ae_strongly_measurable (fun x => (↑n : ℝ)⁻¹) μ)
   · obtain ⟨δ, hδ₁, hδ₂⟩ := hf₂ hε
     refine' ⟨δ, hδ₁, fun n s hs hle => _⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/d4437c68c8d350fc9d4e95e1e174409db35e30d7

@@ -522,7 +522,7 @@ theorem snorm_sub_le_of_dist_bdd {p : ℝ≥0∞} (hp' : p ≠ ∞) {s : Set α}
 #align measure_theory.snorm_sub_le_of_dist_bdd MeasureTheory.snorm_sub_le_of_dist_bdd
 
 /-- A sequence of uniformly integrable functions which converges μ-a.e. converges in Lp. -/
-theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
+theorem tendsto_Lp_of_tendsto_ae_of_meas [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
     {f : ℕ → α → β} {g : α → β} (hf : ∀ n, StronglyMeasurable (f n)) (hg : StronglyMeasurable g)
     (hg' : Memℒp g p μ) (hui : UnifIntegrable f p μ)
     (hfg : ∀ᵐ x ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))) :
@@ -609,7 +609,7 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp
 #align measure_theory.tendsto_Lp_of_tendsto_ae_of_meas MeasureTheory.tendsto_Lp_of_tendsto_ae_of_meas
 
 /-- A sequence of uniformly integrable functions which converges μ-a.e. converges in Lp. -/
-theorem tendsto_Lp_of_tendsto_ae [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ℕ → α → β}
+theorem tendsto_Lp_of_tendsto_ae [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ℕ → α → β}
     {g : α → β} (hf : ∀ n, AeStronglyMeasurable (f n) μ) (hg : Memℒp g p μ)
     (hui : UnifIntegrable f p μ) (hfg : ∀ᵐ x ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))) :
     Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0) :=
@@ -669,7 +669,7 @@ theorem unifIntegrable_of_tendsto_Lp (hp : 1 ≤ p) (hp' : p ≠ ∞) (hf : ∀
 /-- Forward direction of Vitali's convergence theorem: if `f` is a sequence of uniformly integrable
 functions that converge in measure to some function `g` in a finite measure space, then `f`
 converge in Lp to `g`. -/
-theorem tendsto_Lp_of_tendstoInMeasure [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
+theorem tendsto_Lp_of_tendstoInMeasure [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
     (hf : ∀ n, AeStronglyMeasurable (f n) μ) (hg : Memℒp g p μ) (hui : UnifIntegrable f p μ)
     (hfg : TendstoInMeasure μ f atTop g) : Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0) :=
   by
@@ -686,7 +686,7 @@ theorem tendsto_Lp_of_tendstoInMeasure [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp'
 
 /-- **Vitali's convergence theorem**: A sequence of functions `f` converges to `g` in Lp if and
 only if it is uniformly integrable and converges to `g` in measure. -/
-theorem tendstoInMeasure_iff_tendsto_Lp [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
+theorem tendstoInMeasure_iff_tendsto_Lp [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
     (hf : ∀ n, Memℒp (f n) p μ) (hg : Memℒp g p μ) :
     TendstoInMeasure μ f atTop g ∧ UnifIntegrable f p μ ↔
       Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0) :=
@@ -884,7 +884,7 @@ theorem uniformIntegrable_const {g : α → β} (hp : 1 ≤ p) (hp_ne_top : p 
 
 /-- This lemma is superceded by `uniform_integrable_of` which only requires
 `ae_strongly_measurable`. -/
-theorem uniformIntegrable_of' [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
+theorem uniformIntegrable_of' [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
     (hf : ∀ i, StronglyMeasurable (f i))
     (h :
       ∀ ε : ℝ,
@@ -940,7 +940,7 @@ theorem uniformIntegrable_of' [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ 
 
 /-- A sequene of functions `(fₙ)` is uniformly integrable in the probability sense if for all
 `ε > 0`, there exists some `C` such that `∫ x in {|fₙ| ≥ C}, fₙ x ∂μ ≤ ε` for all `n`. -/
-theorem uniformIntegrable_of [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
+theorem uniformIntegrable_of [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
     (hf : ∀ i, AeStronglyMeasurable (f i) μ)
     (h :
       ∀ ε : ℝ,
@@ -1028,7 +1028,7 @@ theorem UniformIntegrable.spec (hp : p ≠ 0) (hp' : p ≠ ∞) (hfu : UniformIn
 
 /-- The definition of uniform integrable in mathlib is equivalent to the definition commonly
 found in literature. -/
-theorem uniformIntegrable_iff [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞) :
+theorem uniformIntegrable_iff [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞) :
     UniformIntegrable f p μ ↔
       (∀ i, AeStronglyMeasurable (f i) μ) ∧
         ∀ ε : ℝ,

mathlib commit https://github.com/leanprover-community/mathlib/commit/92c69b77c5a7dc0f7eeddb552508633305157caa

@@ -141,20 +141,20 @@ protected theorem sub (hf : UnifIntegrable f p μ) (hg : UnifIntegrable g p μ)
   exact hf.add hg.neg hp hf_meas fun i => (hg_meas i).neg
 #align measure_theory.unif_integrable.sub MeasureTheory.UnifIntegrable.sub
 
-protected theorem aeEq (hf : UnifIntegrable f p μ) (hfg : ∀ n, f n =ᵐ[μ] g n) :
+protected theorem ae_eq (hf : UnifIntegrable f p μ) (hfg : ∀ n, f n =ᵐ[μ] g n) :
     UnifIntegrable g p μ := by
   intro ε hε
   obtain ⟨δ, hδ_pos, hfδ⟩ := hf hε
   refine' ⟨δ, hδ_pos, fun n s hs hμs => (le_of_eq <| snorm_congr_ae _).trans (hfδ n s hs hμs)⟩
   filter_upwards [hfg n]with x hx
   simp_rw [indicator_apply, hx]
-#align measure_theory.unif_integrable.ae_eq MeasureTheory.UnifIntegrable.aeEq
+#align measure_theory.unif_integrable.ae_eq MeasureTheory.UnifIntegrable.ae_eq
 
 end UnifIntegrable
 
-theorem unifIntegrableZeroMeas [MeasurableSpace α] {p : ℝ≥0∞} {f : ι → α → β} :
+theorem unifIntegrable_zero_meas [MeasurableSpace α] {p : ℝ≥0∞} {f : ι → α → β} :
     UnifIntegrable f p (0 : Measure α) := fun ε hε => ⟨1, one_pos, fun i s hs hμs => by simp⟩
-#align measure_theory.unif_integrable_zero_meas MeasureTheory.unifIntegrableZeroMeas
+#align measure_theory.unif_integrable_zero_meas MeasureTheory.unifIntegrable_zero_meas
 
 theorem unifIntegrable_congr_ae {p : ℝ≥0∞} {f g : ι → α → β} (hfg : ∀ n, f n =ᵐ[μ] g n) :
     UnifIntegrable f p μ ↔ UnifIntegrable g p μ :=
@@ -437,15 +437,15 @@ theorem Memℒp.snorm_indicator_le (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) (hf :
 #align measure_theory.mem_ℒp.snorm_indicator_le MeasureTheory.Memℒp.snorm_indicator_le
 
 /-- A constant function is uniformly integrable. -/
-theorem unifIntegrableConst {g : α → β} (hp : 1 ≤ p) (hp_ne_top : p ≠ ∞) (hg : Memℒp g p μ) :
+theorem unifIntegrable_const {g : α → β} (hp : 1 ≤ p) (hp_ne_top : p ≠ ∞) (hg : Memℒp g p μ) :
     UnifIntegrable (fun n : ι => g) p μ := by
   intro ε hε
   obtain ⟨δ, hδ_pos, hgδ⟩ := hg.snorm_indicator_le μ hp hp_ne_top hε
   exact ⟨δ, hδ_pos, fun i => hgδ⟩
-#align measure_theory.unif_integrable_const MeasureTheory.unifIntegrableConst
+#align measure_theory.unif_integrable_const MeasureTheory.unifIntegrable_const
 
 /-- A single function is uniformly integrable. -/
-theorem unifIntegrableSubsingleton [Subsingleton ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞)
+theorem unifIntegrable_subsingleton [Subsingleton ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞)
     {f : ι → α → β} (hf : ∀ i, Memℒp (f i) p μ) : UnifIntegrable f p μ :=
   by
   intro ε hε
@@ -455,11 +455,11 @@ theorem unifIntegrableSubsingleton [Subsingleton ι] (hp_one : 1 ≤ p) (hp_top
     refine' ⟨δ, hδpos, fun j s hs hμs => _⟩
     convert hδ s hs hμs
   · exact ⟨1, zero_lt_one, fun i => False.elim <| hι <| Nonempty.intro i⟩
-#align measure_theory.unif_integrable_subsingleton MeasureTheory.unifIntegrableSubsingleton
+#align measure_theory.unif_integrable_subsingleton MeasureTheory.unifIntegrable_subsingleton
 
 /-- This lemma is less general than `measure_theory.unif_integrable_fintype` which applies to
 all sequences indexed by a finite type. -/
-theorem unifIntegrableFin (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) {n : ℕ} {f : Fin n → α → β}
+theorem unifIntegrable_fin (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) {n : ℕ} {f : Fin n → α → β}
     (hf : ∀ i, Memℒp (f i) p μ) : UnifIntegrable f p μ :=
   by
   revert f
@@ -482,10 +482,10 @@ theorem unifIntegrableFin (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) {n : ℕ} {f :
       rw [Nat.lt_succ_iff] at hi'
       rw [not_lt] at hi
       simp [← le_antisymm hi' hi]
-#align measure_theory.unif_integrable_fin MeasureTheory.unifIntegrableFin
+#align measure_theory.unif_integrable_fin MeasureTheory.unifIntegrable_fin
 
 /-- A finite sequence of Lp functions is uniformly integrable. -/
-theorem unifIntegrableFinite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) {f : ι → α → β}
+theorem unifIntegrable_finite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) {f : ι → α → β}
     (hf : ∀ i, Memℒp (f i) p μ) : UnifIntegrable f p μ :=
   by
   obtain ⟨n, hn⟩ := Finite.exists_equiv_fin ι
@@ -497,7 +497,7 @@ theorem unifIntegrableFinite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞)
   specialize hδ (hn.some i) s hs hμs
   simp_rw [hgeq, Function.comp_apply, Equiv.symm_apply_apply] at hδ
   assumption
-#align measure_theory.unif_integrable_finite MeasureTheory.unifIntegrableFinite
+#align measure_theory.unif_integrable_finite MeasureTheory.unifIntegrable_finite
 
 end
 
@@ -634,7 +634,7 @@ theorem tendsto_Lp_of_tendsto_ae [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p 
 
 variable {f : ℕ → α → β} {g : α → β}
 
-theorem unifIntegrableOfTendstoLpZero (hp : 1 ≤ p) (hp' : p ≠ ∞) (hf : ∀ n, Memℒp (f n) p μ)
+theorem unifIntegrable_of_tendsto_Lp_zero (hp : 1 ≤ p) (hp' : p ≠ ∞) (hf : ∀ n, Memℒp (f n) p μ)
     (hf_tendsto : Tendsto (fun n => snorm (f n) p μ) atTop (𝓝 0)) : UnifIntegrable f p μ :=
   by
   intro ε hε
@@ -647,10 +647,10 @@ theorem unifIntegrableOfTendstoLpZero (hp : 1 ≤ p) (hp' : p ≠ ∞) (hf : ∀
   by_cases hn : n < N
   · exact hδ₁ ⟨n, hn⟩ s hs hμs
   · exact (snorm_indicator_le _).trans (hN n (not_lt.1 hn))
-#align measure_theory.unif_integrable_of_tendsto_Lp_zero MeasureTheory.unifIntegrableOfTendstoLpZero
+#align measure_theory.unif_integrable_of_tendsto_Lp_zero MeasureTheory.unifIntegrable_of_tendsto_Lp_zero
 
 /-- Convergence in Lp implies uniform integrability. -/
-theorem unifIntegrableOfTendstoLp (hp : 1 ≤ p) (hp' : p ≠ ∞) (hf : ∀ n, Memℒp (f n) p μ)
+theorem unifIntegrable_of_tendsto_Lp (hp : 1 ≤ p) (hp' : p ≠ ∞) (hf : ∀ n, Memℒp (f n) p μ)
     (hg : Memℒp g p μ) (hfg : Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0)) :
     UnifIntegrable f p μ :=
   by
@@ -664,7 +664,7 @@ theorem unifIntegrableOfTendstoLp (hp : 1 ≤ p) (hp' : p ≠ ∞) (hf : ∀ n,
       (hf n).1.sub hg.ae_strongly_measurable
   · exact unif_integrable_const μ hp hp' hg
   · exact unif_integrable_of_tendsto_Lp_zero μ hp hp' (fun n => (hf n).sub hg) hfg
-#align measure_theory.unif_integrable_of_tendsto_Lp MeasureTheory.unifIntegrableOfTendstoLp
+#align measure_theory.unif_integrable_of_tendsto_Lp MeasureTheory.unifIntegrable_of_tendsto_Lp
 
 /-- Forward direction of Vitali's convergence theorem: if `f` is a sequence of uniformly integrable
 functions that converge in measure to some function `g` in a finite measure space, then `f`
@@ -691,13 +691,13 @@ theorem tendstoInMeasure_iff_tendsto_Lp [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp'
     TendstoInMeasure μ f atTop g ∧ UnifIntegrable f p μ ↔
       Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0) :=
   ⟨fun h => tendsto_Lp_of_tendstoInMeasure μ hp hp' (fun n => (hf n).1) hg h.2 h.1, fun h =>
-    ⟨tendstoInMeasureOfTendstoSnorm (lt_of_lt_of_le zero_lt_one hp).Ne.symm
+    ⟨tendstoInMeasure_of_tendsto_snorm (lt_of_lt_of_le zero_lt_one hp).Ne.symm
         (fun n => (hf n).AeStronglyMeasurable) hg.AeStronglyMeasurable h,
-      unifIntegrableOfTendstoLp μ hp hp' hf hg h⟩⟩
+      unifIntegrable_of_tendsto_Lp μ hp hp' hf hg h⟩⟩
 #align measure_theory.tendsto_in_measure_iff_tendsto_Lp MeasureTheory.tendstoInMeasure_iff_tendsto_Lp
 
 /-- This lemma is superceded by `unif_integrable_of` which do not require `C` to be positive. -/
-theorem unifIntegrableOf' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β}
+theorem unifIntegrable_of' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β}
     (hf : ∀ i, StronglyMeasurable (f i))
     (h :
       ∀ ε : ℝ,
@@ -781,9 +781,9 @@ theorem unifIntegrableOf' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β
       rw [← ENNReal.ofReal_add (half_pos hε).le (half_pos hε).le, add_halves]
       exact le_rfl
     
-#align measure_theory.unif_integrable_of' MeasureTheory.unifIntegrableOf'
+#align measure_theory.unif_integrable_of' MeasureTheory.unifIntegrable_of'
 
-theorem unifIntegrableOf (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β}
+theorem unifIntegrable_of (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β}
     (hf : ∀ i, AeStronglyMeasurable (f i) μ)
     (h :
       ∀ ε : ℝ,
@@ -810,7 +810,7 @@ theorem unifIntegrableOf (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β}
   exact
     indicator_le_indicator_of_subset (fun x hx => le_trans (le_max_left _ _) hx)
       (fun _ => norm_nonneg _) _
-#align measure_theory.unif_integrable_of MeasureTheory.unifIntegrableOf
+#align measure_theory.unif_integrable_of MeasureTheory.unifIntegrable_of
 
 end UnifIntegrable
 
@@ -829,19 +829,19 @@ In this section, we will develope some API for `uniform_integrable` and prove th
 
 variable {p : ℝ≥0∞} {f : ι → α → β}
 
-theorem uniformIntegrableZeroMeas [MeasurableSpace α] : UniformIntegrable f p (0 : Measure α) :=
-  ⟨fun n => aeStronglyMeasurableZeroMeasure _, unifIntegrableZeroMeas, 0, fun i =>
+theorem uniformIntegrable_zero_meas [MeasurableSpace α] : UniformIntegrable f p (0 : Measure α) :=
+  ⟨fun n => aeStronglyMeasurable_zero_measure _, unifIntegrable_zero_meas, 0, fun i =>
     snorm_measure_zero.le⟩
-#align measure_theory.uniform_integrable_zero_meas MeasureTheory.uniformIntegrableZeroMeas
+#align measure_theory.uniform_integrable_zero_meas MeasureTheory.uniformIntegrable_zero_meas
 
-theorem UniformIntegrable.aeEq {g : ι → α → β} (hf : UniformIntegrable f p μ)
+theorem UniformIntegrable.ae_eq {g : ι → α → β} (hf : UniformIntegrable f p μ)
     (hfg : ∀ n, f n =ᵐ[μ] g n) : UniformIntegrable g p μ :=
   by
   obtain ⟨hfm, hunif, C, hC⟩ := hf
   refine' ⟨fun i => (hfm i).congr (hfg i), (unif_integrable_congr_ae hfg).1 hunif, C, fun i => _⟩
   rw [← snorm_congr_ae (hfg i)]
   exact hC i
-#align measure_theory.uniform_integrable.ae_eq MeasureTheory.UniformIntegrable.aeEq
+#align measure_theory.uniform_integrable.ae_eq MeasureTheory.UniformIntegrable.ae_eq
 
 theorem uniformIntegrable_congr_ae {g : ι → α → β} (hfg : ∀ n, f n =ᵐ[μ] g n) :
     UniformIntegrable f p μ ↔ UniformIntegrable g p μ :=
@@ -849,7 +849,7 @@ theorem uniformIntegrable_congr_ae {g : ι → α → β} (hfg : ∀ n, f n =ᵐ
 #align measure_theory.uniform_integrable_congr_ae MeasureTheory.uniformIntegrable_congr_ae
 
 /-- A finite sequence of Lp functions is uniformly integrable in the probability sense. -/
-theorem uniformIntegrableFinite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞)
+theorem uniformIntegrable_finite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞)
     (hf : ∀ i, Memℒp (f i) p μ) : UniformIntegrable f p μ :=
   by
   cases nonempty_fintype ι
@@ -867,24 +867,24 @@ theorem uniformIntegrableFinite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠ 
       obtain ⟨i, -, rfl⟩ := hy
       exact hf i
   · exact ⟨0, fun i => False.elim <| hι <| Nonempty.intro i⟩
-#align measure_theory.uniform_integrable_finite MeasureTheory.uniformIntegrableFinite
+#align measure_theory.uniform_integrable_finite MeasureTheory.uniformIntegrable_finite
 
 /-- A single function is uniformly integrable in the probability sense. -/
-theorem uniformIntegrableSubsingleton [Subsingleton ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞)
+theorem uniformIntegrable_subsingleton [Subsingleton ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞)
     (hf : ∀ i, Memℒp (f i) p μ) : UniformIntegrable f p μ :=
-  uniformIntegrableFinite hp_one hp_top hf
-#align measure_theory.uniform_integrable_subsingleton MeasureTheory.uniformIntegrableSubsingleton
+  uniformIntegrable_finite hp_one hp_top hf
+#align measure_theory.uniform_integrable_subsingleton MeasureTheory.uniformIntegrable_subsingleton
 
 /-- A constant sequence of functions is uniformly integrable in the probability sense. -/
-theorem uniformIntegrableConst {g : α → β} (hp : 1 ≤ p) (hp_ne_top : p ≠ ∞) (hg : Memℒp g p μ) :
+theorem uniformIntegrable_const {g : α → β} (hp : 1 ≤ p) (hp_ne_top : p ≠ ∞) (hg : Memℒp g p μ) :
     UniformIntegrable (fun n : ι => g) p μ :=
-  ⟨fun i => hg.1, unifIntegrableConst μ hp hp_ne_top hg,
+  ⟨fun i => hg.1, unifIntegrable_const μ hp hp_ne_top hg,
     ⟨(snorm g p μ).toNNReal, fun i => le_of_eq (ENNReal.coe_toNNReal hg.2.Ne).symm⟩⟩
-#align measure_theory.uniform_integrable_const MeasureTheory.uniformIntegrableConst
+#align measure_theory.uniform_integrable_const MeasureTheory.uniformIntegrable_const
 
 /-- This lemma is superceded by `uniform_integrable_of` which only requires
 `ae_strongly_measurable`. -/
-theorem uniformIntegrableOf' [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
+theorem uniformIntegrable_of' [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
     (hf : ∀ i, StronglyMeasurable (f i))
     (h :
       ∀ ε : ℝ,
@@ -936,11 +936,11 @@ theorem uniformIntegrableOf' [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ 
                 (measure_lt_top _ _).Ne),
             ENNReal.one_ne_top⟩
     
-#align measure_theory.uniform_integrable_of' MeasureTheory.uniformIntegrableOf'
+#align measure_theory.uniform_integrable_of' MeasureTheory.uniformIntegrable_of'
 
 /-- A sequene of functions `(fₙ)` is uniformly integrable in the probability sense if for all
 `ε > 0`, there exists some `C` such that `∫ x in {|fₙ| ≥ C}, fₙ x ∂μ ≤ ε` for all `n`. -/
-theorem uniformIntegrableOf [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
+theorem uniformIntegrable_of [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
     (hf : ∀ i, AeStronglyMeasurable (f i) μ)
     (h :
       ∀ ε : ℝ,
@@ -960,7 +960,7 @@ theorem uniformIntegrableOf [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞
     rwa [mem_set_of, hx] at hfx
   · rw [indicator_of_not_mem hfx, indicator_of_not_mem]
     rwa [mem_set_of, hx] at hfx
-#align measure_theory.uniform_integrable_of MeasureTheory.uniformIntegrableOf
+#align measure_theory.uniform_integrable_of MeasureTheory.uniformIntegrable_of
 
 /-- This lemma is superceded by `uniform_integrable.spec` which does not require measurability. -/
 theorem UniformIntegrable.spec' (hp : p ≠ 0) (hp' : p ≠ ∞) (hf : ∀ i, StronglyMeasurable (f i))
@@ -1035,18 +1035,18 @@ theorem uniformIntegrable_iff [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ 
           0 < ε →
             ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε :=
   ⟨fun h => ⟨h.1, fun ε => h.spec (lt_of_lt_of_le zero_lt_one hp).Ne.symm hp'⟩, fun h =>
-    uniformIntegrableOf hp hp' h.1 h.2⟩
+    uniformIntegrable_of hp hp' h.1 h.2⟩
 #align measure_theory.uniform_integrable_iff MeasureTheory.uniformIntegrable_iff
 
 /-- The averaging of a uniformly integrable sequence is also uniformly integrable. -/
-theorem uniformIntegrableAverage (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf : UniformIntegrable f p μ) :
+theorem uniformIntegrable_average (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf : UniformIntegrable f p μ) :
     UniformIntegrable (fun n => (∑ i in Finset.range n, f i) / n) p μ :=
   by
   obtain ⟨hf₁, hf₂, hf₃⟩ := hf
   refine' ⟨fun n => _, fun ε hε => _, _⟩
   · simp_rw [div_eq_mul_inv]
     exact
-      (Finset.ae_strongly_measurable_sum' _ fun i _ => hf₁ i).mul
+      (Finset.aeStronglyMeasurable_sum' _ fun i _ => hf₁ i).mul
         (ae_strongly_measurable_const : ae_strongly_measurable (fun x => (↑n : ℝ)⁻¹) μ)
   · obtain ⟨δ, hδ₁, hδ₂⟩ := hf₂ hε
     refine' ⟨δ, hδ₁, fun n s hs hle => _⟩
@@ -1091,7 +1091,7 @@ theorem uniformIntegrableAverage (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf : U
         ENNReal.inv_mul_cancel _ (ENNReal.nat_ne_top _), one_mul]
       · exact le_rfl
       all_goals simpa only [Ne.def, Nat.cast_eq_zero]
-#align measure_theory.uniform_integrable_average MeasureTheory.uniformIntegrableAverage
+#align measure_theory.uniform_integrable_average MeasureTheory.uniformIntegrable_average
 
 end UniformIntegrable
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -1061,7 +1061,7 @@ theorem uniformIntegrableAverage (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf : U
       · rfl
     simp_rw [this, snorm_const_smul, ← Finset.mul_sum, nnnorm_inv, Real.nnnorm_coe_nat]
     by_cases hn : (↑(↑n : ℝ≥0)⁻¹ : ℝ≥0∞) = 0
-    · simp only [hn, zero_mul, zero_le]
+    · simp only [hn, MulZeroClass.zero_mul, zero_le]
     refine' le_trans _ (_ : ↑(↑n : ℝ≥0)⁻¹ * n • ENNReal.ofReal ε ≤ ENNReal.ofReal ε)
     · refine' (ENNReal.mul_le_mul_left hn ENNReal.coe_ne_top).2 _
       conv_rhs => rw [← Finset.card_range n]
@@ -1081,7 +1081,7 @@ theorem uniformIntegrableAverage (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf : U
       simp only [mul_comm, Pi.smul_apply, Algebra.id.smul_eq_mul]
     simp_rw [this, snorm_const_smul, ← Finset.mul_sum, nnnorm_inv, Real.nnnorm_coe_nat]
     by_cases hn : (↑(↑n : ℝ≥0)⁻¹ : ℝ≥0∞) = 0
-    · simp only [hn, zero_mul, zero_le]
+    · simp only [hn, MulZeroClass.zero_mul, zero_le]
     refine' le_trans _ (_ : ↑(↑n : ℝ≥0)⁻¹ * (n • C : ℝ≥0∞) ≤ C)
     · refine' (ENNReal.mul_le_mul_left hn ENNReal.coe_ne_top).2 _
       conv_rhs => rw [← Finset.card_range n]

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -328,7 +328,7 @@ theorem Memℒp.snorm_indicator_norm_ge_pos_le (hf : Memℒp f p μ) (hmeas : St
 
 end
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:75:38: in filter_upwards #[[], [], []]: ./././Mathport/Syntax/Translate/Basic.lean:349:22: unsupported: parse error @ arg 0: next failed, no more args -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], [], []]: ./././Mathport/Syntax/Translate/Basic.lean:349:22: unsupported: parse error @ arg 0: next failed, no more args -/
 theorem snorm_indicator_le_of_bound {f : α → β} (hp_top : p ≠ ∞) {ε : ℝ} (hε : 0 < ε) {M : ℝ}
     (hf : ∀ x, ‖f x‖ < M) :
     ∃ (δ : ℝ)(hδ : 0 < δ),
@@ -350,7 +350,7 @@ theorem snorm_indicator_le_of_bound {f : α → β} (hp_top : p ≠ ∞) {ε : 
   have haebdd : ∀ᵐ x ∂μ.restrict s, ‖f x‖ ≤ M :=
     by
     trace
-      "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:75:38: in filter_upwards #[[], [], []]: ./././Mathport/Syntax/Translate/Basic.lean:349:22: unsupported: parse error @ arg 0: next failed, no more args"
+      "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], [], []]: ./././Mathport/Syntax/Translate/Basic.lean:349:22: unsupported: parse error @ arg 0: next failed, no more args"
     exact fun x => (hf x).le
   refine' le_trans (snorm_le_of_ae_bound haebdd) _
   rw [measure.restrict_apply MeasurableSet.univ, univ_inter, ←

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
 
 ! This file was ported from Lean 3 source module measure_theory.function.uniform_integrable
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -517,7 +517,7 @@ theorem snorm_sub_le_of_dist_bdd {p : ℝ≥0∞} (hp' : p ≠ ∞) {s : Set α}
     · simp [indicator_of_not_mem hx]
   refine' le_trans (snorm_mono this) _
   rw [snorm_indicator_const hs hp hp']
-  refine' ENNReal.mul_le_mul (le_of_eq _) le_rfl
+  refine' mul_le_mul_right' (le_of_eq _) _
   rw [← ofReal_norm_eq_coe_nnnorm, Real.norm_eq_abs, abs_of_nonneg hc]
 #align measure_theory.snorm_sub_le_of_dist_bdd MeasureTheory.snorm_sub_le_of_dist_bdd
 
@@ -541,7 +541,7 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp
   have hdivp : 0 ≤ 1 / p.to_real := by
     refine' one_div_nonneg.2 _
     rw [← ENNReal.zero_toReal, ENNReal.toReal_le_toReal ENNReal.zero_ne_top hp']
-    exact le_trans ennreal.zero_lt_one.le hp
+    exact le_trans (zero_le _) hp
   have hpow : 0 < measure_univ_nnreal μ ^ (1 / p.to_real) :=
     Real.rpow_pos_of_pos (measure_univ_nnreal_pos hμ) _
   obtain ⟨δ₁, hδ₁, hsnorm₁⟩ := hui hε'
@@ -691,7 +691,7 @@ theorem tendstoInMeasure_iff_tendsto_Lp [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp'
     TendstoInMeasure μ f atTop g ∧ UnifIntegrable f p μ ↔
       Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0) :=
   ⟨fun h => tendsto_Lp_of_tendstoInMeasure μ hp hp' (fun n => (hf n).1) hg h.2 h.1, fun h =>
-    ⟨tendstoInMeasureOfTendstoSnorm (lt_of_lt_of_le ENNReal.zero_lt_one hp).Ne.symm
+    ⟨tendstoInMeasureOfTendstoSnorm (lt_of_lt_of_le zero_lt_one hp).Ne.symm
         (fun n => (hf n).AeStronglyMeasurable) hg.AeStronglyMeasurable h,
       unifIntegrableOfTendstoLp μ hp hp' hf hg h⟩⟩
 #align measure_theory.tendsto_in_measure_iff_tendsto_Lp MeasureTheory.tendstoInMeasure_iff_tendsto_Lp
@@ -706,7 +706,7 @@ theorem unifIntegrableOf' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β
             0 < C ∧ ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε) :
     UnifIntegrable f p μ :=
   by
-  have hpzero := (lt_of_lt_of_le ENNReal.zero_lt_one hp).Ne.symm
+  have hpzero := (lt_of_lt_of_le zero_lt_one hp).Ne.symm
   by_cases hμ : μ Set.univ = 0
   · rw [measure.measure_univ_eq_zero] at hμ
     exact hμ.symm ▸ unif_integrable_zero_meas
@@ -984,7 +984,7 @@ theorem UniformIntegrable.spec' (hp : p ≠ 0) (hp' : p ≠ ∞) (hf : ∀ i, St
           rw [ENNReal.smul_def, ENNReal.smul_def, smul_eq_mul, smul_eq_mul]
           simp_rw [ENNReal.ofReal_coe_nnreal] at hℐ
           refine'
-            ENNReal.mul_le_mul le_rfl
+            mul_le_mul' le_rfl
               (ENNReal.rpow_le_rpow (hℐ C).le (one_div_nonneg.2 ENNReal.toReal_nonneg))
         _ ≤ snorm ({ x | C ≤ ‖f (ℐ C) x‖₊ }.indicator (f (ℐ C))) p μ :=
           by
@@ -1034,7 +1034,7 @@ theorem uniformIntegrable_iff [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ 
         ∀ ε : ℝ,
           0 < ε →
             ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε :=
-  ⟨fun h => ⟨h.1, fun ε => h.spec (lt_of_lt_of_le ENNReal.zero_lt_one hp).Ne.symm hp'⟩, fun h =>
+  ⟨fun h => ⟨h.1, fun ε => h.spec (lt_of_lt_of_le zero_lt_one hp).Ne.symm hp'⟩, fun h =>
     uniformIntegrableOf hp hp' h.1 h.2⟩
 #align measure_theory.uniform_integrable_iff MeasureTheory.uniformIntegrable_iff
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

@@ -50,7 +50,7 @@ uniform integrable, uniformly absolutely continuous integral, Vitali convergence
 
 noncomputable section
 
-open Classical MeasureTheory NNReal Ennreal Topology BigOperators
+open Classical MeasureTheory NNReal ENNReal Topology BigOperators
 
 namespace MeasureTheory
 
@@ -69,7 +69,7 @@ def UnifIntegrable {m : MeasurableSpace α} (f : ι → α → β) (p : ℝ≥0
   ∀ ⦃ε : ℝ⦄ (hε : 0 < ε),
     ∃ (δ : ℝ)(hδ : 0 < δ),
       ∀ i s,
-        MeasurableSet s → μ s ≤ Ennreal.ofReal δ → snorm (s.indicator (f i)) p μ ≤ Ennreal.ofReal ε
+        MeasurableSet s → μ s ≤ ENNReal.ofReal δ → snorm (s.indicator (f i)) p μ ≤ ENNReal.ofReal ε
 #align measure_theory.unif_integrable MeasureTheory.UnifIntegrable
 
 /-- In probability theory, a family of measurable functions is uniformly integrable if it is
@@ -94,7 +94,7 @@ protected theorem memℒp {f : ι → α → β} {p : ℝ≥0∞} (hf : UniformI
     Memℒp (f i) p μ :=
   ⟨hf.1 i,
     let ⟨_, _, hC⟩ := hf.2
-    lt_of_le_of_lt (hC i) Ennreal.coe_lt_top⟩
+    lt_of_le_of_lt (hC i) ENNReal.coe_lt_top⟩
 #align measure_theory.uniform_integrable.mem_ℒp MeasureTheory.UniformIntegrable.memℒp
 
 end UniformIntegrable
@@ -120,12 +120,12 @@ protected theorem add (hf : UnifIntegrable f p μ) (hg : UnifIntegrable g p μ)
   refine' ⟨min δ₁ δ₂, lt_min hδ₁_pos hδ₂_pos, fun i s hs hμs => _⟩
   simp_rw [Pi.add_apply, indicator_add']
   refine' (snorm_add_le ((hf_meas i).indicator hs) ((hg_meas i).indicator hs) hp).trans _
-  have hε_halves : Ennreal.ofReal ε = Ennreal.ofReal (ε / 2) + Ennreal.ofReal (ε / 2) := by
-    rw [← Ennreal.ofReal_add hε2.le hε2.le, add_halves]
+  have hε_halves : ENNReal.ofReal ε = ENNReal.ofReal (ε / 2) + ENNReal.ofReal (ε / 2) := by
+    rw [← ENNReal.ofReal_add hε2.le hε2.le, add_halves]
   rw [hε_halves]
   exact
-    add_le_add (hfδ₁ i s hs (hμs.trans (Ennreal.ofReal_le_ofReal (min_le_left _ _))))
-      (hgδ₂ i s hs (hμs.trans (Ennreal.ofReal_le_ofReal (min_le_right _ _))))
+    add_le_add (hfδ₁ i s hs (hμs.trans (ENNReal.ofReal_le_ofReal (min_le_left _ _))))
+      (hgδ₂ i s hs (hμs.trans (ENNReal.ofReal_le_ofReal (min_le_right _ _))))
 #align measure_theory.unif_integrable.add MeasureTheory.UnifIntegrable.add
 
 protected theorem neg (hf : UnifIntegrable f p μ) : UnifIntegrable (-f) p μ :=
@@ -183,7 +183,7 @@ variable {f : α → β}
 as the latter provides `0 ≤ M` and does not require the measurability of `f`. -/
 theorem Memℒp.integral_indicator_norm_ge_le (hf : Memℒp f 1 μ) (hmeas : StronglyMeasurable f)
     {ε : ℝ} (hε : 0 < ε) :
-    ∃ M : ℝ, (∫⁻ x, ‖{ x | M ≤ ‖f x‖₊ }.indicator f x‖₊ ∂μ) ≤ Ennreal.ofReal ε :=
+    ∃ M : ℝ, (∫⁻ x, ‖{ x | M ≤ ‖f x‖₊ }.indicator f x‖₊ ∂μ) ≤ ENNReal.ofReal ε :=
   by
   have htendsto :
     ∀ᵐ x ∂μ, tendsto (fun M : ℕ => { x | (M : ℝ) ≤ ‖f x‖₊ }.indicator f x) at_top (𝓝 0) :=
@@ -200,14 +200,14 @@ theorem Memℒp.integral_indicator_norm_ge_le (hf : Memℒp f 1 μ) (hmeas : Str
     rw [mem_ℒp_one_iff_integrable] at hf
     exact hf.norm.2
   have := tendsto_lintegral_norm_of_dominated_convergence hmeas hbound _ htendsto
-  · rw [Ennreal.tendsto_atTop_zero] at this
-    obtain ⟨M, hM⟩ := this (Ennreal.ofReal ε) (Ennreal.ofReal_pos.2 hε)
+  · rw [ENNReal.tendsto_atTop_zero] at this
+    obtain ⟨M, hM⟩ := this (ENNReal.ofReal ε) (ENNReal.ofReal_pos.2 hε)
     simp only [true_and_iff, ge_iff_le, zero_tsub, zero_le, sub_zero, zero_add, coe_nnnorm,
       mem_Icc] at hM
     refine' ⟨M, _⟩
     convert hM M le_rfl
     ext1 x
-    simp only [coe_nnnorm, Ennreal.ofReal_eq_coe_nNReal (norm_nonneg _)]
+    simp only [coe_nnnorm, ENNReal.ofReal_eq_coe_nnreal (norm_nonneg _)]
     rfl
   · refine' fun n => univ_mem' (id fun x => _)
     by_cases hx : (n : ℝ) ≤ ‖f x‖
@@ -223,13 +223,13 @@ theorem Memℒp.integral_indicator_norm_ge_le (hf : Memℒp f 1 μ) (hmeas : Str
 which does not require measurability. -/
 theorem Memℒp.integral_indicator_norm_ge_nonneg_le_of_meas (hf : Memℒp f 1 μ)
     (hmeas : StronglyMeasurable f) {ε : ℝ} (hε : 0 < ε) :
-    ∃ M : ℝ, 0 ≤ M ∧ (∫⁻ x, ‖{ x | M ≤ ‖f x‖₊ }.indicator f x‖₊ ∂μ) ≤ Ennreal.ofReal ε :=
+    ∃ M : ℝ, 0 ≤ M ∧ (∫⁻ x, ‖{ x | M ≤ ‖f x‖₊ }.indicator f x‖₊ ∂μ) ≤ ENNReal.ofReal ε :=
   let ⟨M, hM⟩ := hf.integral_indicator_norm_ge_le μ hmeas hε
   ⟨max M 0, le_max_right _ _, by simpa⟩
 #align measure_theory.mem_ℒp.integral_indicator_norm_ge_nonneg_le_of_meas MeasureTheory.Memℒp.integral_indicator_norm_ge_nonneg_le_of_meas
 
 theorem Memℒp.integral_indicator_norm_ge_nonneg_le (hf : Memℒp f 1 μ) {ε : ℝ} (hε : 0 < ε) :
-    ∃ M : ℝ, 0 ≤ M ∧ (∫⁻ x, ‖{ x | M ≤ ‖f x‖₊ }.indicator f x‖₊ ∂μ) ≤ Ennreal.ofReal ε :=
+    ∃ M : ℝ, 0 ≤ M ∧ (∫⁻ x, ‖{ x | M ≤ ‖f x‖₊ }.indicator f x‖₊ ∂μ) ≤ ENNReal.ofReal ε :=
   by
   have hf_mk : mem_ℒp (hf.1.mk f) 1 μ := (mem_ℒp_congr_ae hf.1.ae_eq_mk).mp hf
   obtain ⟨M, hM_pos, hfM⟩ :=
@@ -237,7 +237,7 @@ theorem Memℒp.integral_indicator_norm_ge_nonneg_le (hf : Memℒp f 1 μ) {ε :
   refine' ⟨M, hM_pos, (le_of_eq _).trans hfM⟩
   refine' lintegral_congr_ae _
   filter_upwards [hf.1.ae_eq_mk]with x hx
-  simp only [indicator_apply, coe_nnnorm, mem_set_of_eq, Ennreal.coe_eq_coe, hx.symm]
+  simp only [indicator_apply, coe_nnnorm, mem_set_of_eq, ENNReal.coe_eq_coe, hx.symm]
 #align measure_theory.mem_ℒp.integral_indicator_norm_ge_nonneg_le MeasureTheory.Memℒp.integral_indicator_norm_ge_nonneg_le
 
 theorem Memℒp.snormEssSup_indicator_norm_ge_eq_zero (hf : Memℒp f ∞ μ)
@@ -253,12 +253,12 @@ theorem Memℒp.snormEssSup_indicator_norm_ge_eq_zero (hf : Memℒp f ∞ μ)
       { x : α | (snorm_ess_sup f μ + 1).toReal ≤ ‖f x‖ } ⊆ { x : α | snorm_ess_sup f μ < ‖f x‖₊ } :=
       by
       intro x hx
-      rw [mem_set_of_eq, ← Ennreal.toReal_lt_toReal hbdd.ne ennreal.coe_lt_top.ne,
-        Ennreal.coe_toReal, coe_nnnorm]
+      rw [mem_set_of_eq, ← ENNReal.toReal_lt_toReal hbdd.ne ennreal.coe_lt_top.ne,
+        ENNReal.coe_toReal, coe_nnnorm]
       refine' lt_of_lt_of_le _ hx
-      rw [Ennreal.toReal_lt_toReal hbdd.ne]
-      · exact Ennreal.lt_add_right hbdd.ne one_ne_zero
-      · exact (Ennreal.add_lt_top.2 ⟨hbdd, Ennreal.one_lt_top⟩).Ne
+      rw [ENNReal.toReal_lt_toReal hbdd.ne]
+      · exact ENNReal.lt_add_right hbdd.ne one_ne_zero
+      · exact (ENNReal.add_lt_top.2 ⟨hbdd, ENNReal.one_lt_top⟩).Ne
     rw [← nonpos_iff_eq_zero]
     refine' (measure_mono this).trans _
     have hle := coe_nnnorm_ae_le_snorm_ess_sup f μ
@@ -271,7 +271,7 @@ theorem Memℒp.snormEssSup_indicator_norm_ge_eq_zero (hf : Memℒp f ∞ μ)
 /- This lemma is slightly weaker than `measure_theory.mem_ℒp.snorm_indicator_norm_ge_pos_le` as the
 latter provides `0 < M`. -/
 theorem Memℒp.snorm_indicator_norm_ge_le (hf : Memℒp f p μ) (hmeas : StronglyMeasurable f) {ε : ℝ}
-    (hε : 0 < ε) : ∃ M : ℝ, snorm ({ x | M ≤ ‖f x‖₊ }.indicator f) p μ ≤ Ennreal.ofReal ε :=
+    (hε : 0 < ε) : ∃ M : ℝ, snorm ({ x | M ≤ ‖f x‖₊ }.indicator f) p μ ≤ ENNReal.ofReal ε :=
   by
   by_cases hp_ne_zero : p = 0
   · refine' ⟨1, hp_ne_zero.symm ▸ _⟩
@@ -285,28 +285,28 @@ theorem Memℒp.snorm_indicator_norm_ge_le (hf : Memℒp f p μ) (hmeas : Strong
     @mem_ℒp.integral_indicator_norm_ge_nonneg_le _ _ _ μ _ (fun x => ‖f x‖ ^ p.to_real)
       (hf.norm_rpow hp_ne_zero hp_ne_top) _ (Real.rpow_pos_of_pos hε p.to_real)
   refine' ⟨M ^ (1 / p.to_real), _⟩
-  rw [snorm_eq_lintegral_rpow_nnnorm hp_ne_zero hp_ne_top, ← Ennreal.rpow_one (Ennreal.ofReal ε)]
-  conv_rhs => rw [← mul_one_div_cancel (Ennreal.toReal_pos hp_ne_zero hp_ne_top).Ne.symm]
-  rw [Ennreal.rpow_mul,
-    Ennreal.rpow_le_rpow_iff (one_div_pos.2 <| Ennreal.toReal_pos hp_ne_zero hp_ne_top),
-    Ennreal.ofReal_rpow_of_pos hε]
+  rw [snorm_eq_lintegral_rpow_nnnorm hp_ne_zero hp_ne_top, ← ENNReal.rpow_one (ENNReal.ofReal ε)]
+  conv_rhs => rw [← mul_one_div_cancel (ENNReal.toReal_pos hp_ne_zero hp_ne_top).Ne.symm]
+  rw [ENNReal.rpow_mul,
+    ENNReal.rpow_le_rpow_iff (one_div_pos.2 <| ENNReal.toReal_pos hp_ne_zero hp_ne_top),
+    ENNReal.ofReal_rpow_of_pos hε]
   convert hM
   ext1 x
-  rw [Ennreal.coe_rpow_of_nonneg _ Ennreal.toReal_nonneg, nnnorm_indicator_eq_indicator_nnnorm,
+  rw [ENNReal.coe_rpow_of_nonneg _ ENNReal.toReal_nonneg, nnnorm_indicator_eq_indicator_nnnorm,
     nnnorm_indicator_eq_indicator_nnnorm]
   have hiff : M ^ (1 / p.to_real) ≤ ‖f x‖₊ ↔ M ≤ ‖‖f x‖ ^ p.to_real‖₊ := by
     rw [coe_nnnorm, coe_nnnorm, Real.norm_rpow_of_nonneg (norm_nonneg _), norm_norm, ←
       Real.rpow_le_rpow_iff hM' (Real.rpow_nonneg_of_nonneg (norm_nonneg _) _)
-        (one_div_pos.2 <| Ennreal.toReal_pos hp_ne_zero hp_ne_top),
+        (one_div_pos.2 <| ENNReal.toReal_pos hp_ne_zero hp_ne_top),
       ← Real.rpow_mul (norm_nonneg _),
-      mul_one_div_cancel (Ennreal.toReal_pos hp_ne_zero hp_ne_top).Ne.symm, Real.rpow_one]
+      mul_one_div_cancel (ENNReal.toReal_pos hp_ne_zero hp_ne_top).Ne.symm, Real.rpow_one]
   by_cases hx : x ∈ { x : α | M ^ (1 / p.to_real) ≤ ‖f x‖₊ }
   · rw [Set.indicator_of_mem hx, Set.indicator_of_mem, Real.nnnorm_of_nonneg]
     rfl
     change _ ≤ _
     rwa [← hiff]
   · rw [Set.indicator_of_not_mem hx, Set.indicator_of_not_mem]
-    · simp [(Ennreal.toReal_pos hp_ne_zero hp_ne_top).Ne.symm]
+    · simp [(ENNReal.toReal_pos hp_ne_zero hp_ne_top).Ne.symm]
     · change ¬_ ≤ _
       rwa [← hiff]
 #align measure_theory.mem_ℒp.snorm_indicator_norm_ge_le MeasureTheory.Memℒp.snorm_indicator_norm_ge_le
@@ -314,7 +314,7 @@ theorem Memℒp.snorm_indicator_norm_ge_le (hf : Memℒp f p μ) (hmeas : Strong
 /-- This lemma implies that a single function is uniformly integrable (in the probability sense). -/
 theorem Memℒp.snorm_indicator_norm_ge_pos_le (hf : Memℒp f p μ) (hmeas : StronglyMeasurable f)
     {ε : ℝ} (hε : 0 < ε) :
-    ∃ M : ℝ, 0 < M ∧ snorm ({ x | M ≤ ‖f x‖₊ }.indicator f) p μ ≤ Ennreal.ofReal ε :=
+    ∃ M : ℝ, 0 < M ∧ snorm ({ x | M ≤ ‖f x‖₊ }.indicator f) p μ ≤ ENNReal.ofReal ε :=
   by
   obtain ⟨M, hM⟩ := hf.snorm_indicator_norm_ge_le μ hmeas hε
   refine'
@@ -333,7 +333,7 @@ theorem snorm_indicator_le_of_bound {f : α → β} (hp_top : p ≠ ∞) {ε : 
     (hf : ∀ x, ‖f x‖ < M) :
     ∃ (δ : ℝ)(hδ : 0 < δ),
       ∀ s,
-        MeasurableSet s → μ s ≤ Ennreal.ofReal δ → snorm (s.indicator f) p μ ≤ Ennreal.ofReal ε :=
+        MeasurableSet s → μ s ≤ ENNReal.ofReal δ → snorm (s.indicator f) p μ ≤ ENNReal.ofReal ε :=
   by
   by_cases hM : M ≤ 0
   · refine' ⟨1, zero_lt_one, fun s hs hμ => _⟩
@@ -354,13 +354,13 @@ theorem snorm_indicator_le_of_bound {f : α → β} (hp_top : p ≠ ∞) {ε : 
     exact fun x => (hf x).le
   refine' le_trans (snorm_le_of_ae_bound haebdd) _
   rw [measure.restrict_apply MeasurableSet.univ, univ_inter, ←
-    Ennreal.le_div_iff_mul_le (Or.inl _) (Or.inl Ennreal.ofReal_ne_top)]
-  · rw [← one_div, Ennreal.rpow_one_div_le_iff (Ennreal.toReal_pos hp hp_top)]
+    ENNReal.le_div_iff_mul_le (Or.inl _) (Or.inl ENNReal.ofReal_ne_top)]
+  · rw [← one_div, ENNReal.rpow_one_div_le_iff (ENNReal.toReal_pos hp hp_top)]
     refine' le_trans hμ _
-    rw [← Ennreal.ofReal_rpow_of_pos (div_pos hε hM),
-      Ennreal.rpow_le_rpow_iff (Ennreal.toReal_pos hp hp_top), Ennreal.ofReal_div_of_pos hM]
+    rw [← ENNReal.ofReal_rpow_of_pos (div_pos hε hM),
+      ENNReal.rpow_le_rpow_iff (ENNReal.toReal_pos hp hp_top), ENNReal.ofReal_div_of_pos hM]
     exact le_rfl
-  · simpa only [Ennreal.ofReal_eq_zero, not_le, Ne.def]
+  · simpa only [ENNReal.ofReal_eq_zero, not_le, Ne.def]
 #align measure_theory.snorm_indicator_le_of_bound MeasureTheory.snorm_indicator_le_of_bound
 
 section
@@ -373,7 +373,7 @@ theorem Memℒp.snorm_indicator_le' (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) (hf
     ∃ (δ : ℝ)(hδ : 0 < δ),
       ∀ s,
         MeasurableSet s →
-          μ s ≤ Ennreal.ofReal δ → snorm (s.indicator f) p μ ≤ 2 * Ennreal.ofReal ε :=
+          μ s ≤ ENNReal.ofReal δ → snorm (s.indicator f) p μ ≤ 2 * ENNReal.ofReal ε :=
   by
   obtain ⟨M, hMpos, hM⟩ := hf.snorm_indicator_norm_ge_pos_le μ hmeas hε
   obtain ⟨δ, hδpos, hδ⟩ :=
@@ -412,12 +412,12 @@ theorem Memℒp.snorm_indicator_le_of_meas (hp_one : 1 ≤ p) (hp_top : p ≠ 
     (hmeas : StronglyMeasurable f) {ε : ℝ} (hε : 0 < ε) :
     ∃ (δ : ℝ)(hδ : 0 < δ),
       ∀ s,
-        MeasurableSet s → μ s ≤ Ennreal.ofReal δ → snorm (s.indicator f) p μ ≤ Ennreal.ofReal ε :=
+        MeasurableSet s → μ s ≤ ENNReal.ofReal δ → snorm (s.indicator f) p μ ≤ ENNReal.ofReal ε :=
   by
   obtain ⟨δ, hδpos, hδ⟩ := hf.snorm_indicator_le' μ hp_one hp_top hmeas (half_pos hε)
   refine' ⟨δ, hδpos, fun s hs hμs => le_trans (hδ s hs hμs) _⟩
-  rw [Ennreal.ofReal_div_of_pos zero_lt_two, (by norm_num : Ennreal.ofReal 2 = 2),
-      Ennreal.mul_div_cancel'] <;>
+  rw [ENNReal.ofReal_div_of_pos zero_lt_two, (by norm_num : ENNReal.ofReal 2 = 2),
+      ENNReal.mul_div_cancel'] <;>
     norm_num
 #align measure_theory.mem_ℒp.snorm_indicator_le_of_meas MeasureTheory.Memℒp.snorm_indicator_le_of_meas
 
@@ -425,7 +425,7 @@ theorem Memℒp.snorm_indicator_le (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) (hf :
     (hε : 0 < ε) :
     ∃ (δ : ℝ)(hδ : 0 < δ),
       ∀ s,
-        MeasurableSet s → μ s ≤ Ennreal.ofReal δ → snorm (s.indicator f) p μ ≤ Ennreal.ofReal ε :=
+        MeasurableSet s → μ s ≤ ENNReal.ofReal δ → snorm (s.indicator f) p μ ≤ ENNReal.ofReal ε :=
   by
   have hℒp := hf
   obtain ⟨⟨f', hf', heq⟩, hnorm⟩ := hf
@@ -473,11 +473,11 @@ theorem unifIntegrableFin (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) {n : ℕ} {f :
   refine' ⟨min δ₁ δ₂, lt_min hδ₁pos hδ₂pos, fun i s hs hμs => _⟩
   by_cases hi : i.val < n
   · rw [(_ : f i = g ⟨i.val, hi⟩)]
-    · exact hδ₁ _ s hs (le_trans hμs <| Ennreal.ofReal_le_ofReal <| min_le_left _ _)
+    · exact hδ₁ _ s hs (le_trans hμs <| ENNReal.ofReal_le_ofReal <| min_le_left _ _)
     · rw [hg]
       simp
   · rw [(_ : i = n)]
-    · exact hδ₂ _ hs (le_trans hμs <| Ennreal.ofReal_le_ofReal <| min_le_right _ _)
+    · exact hδ₂ _ hs (le_trans hμs <| ENNReal.ofReal_le_ofReal <| min_le_right _ _)
     · have hi' := Fin.is_lt i
       rw [Nat.lt_succ_iff] at hi'
       rw [not_lt] at hi
@@ -503,7 +503,7 @@ end
 
 theorem snorm_sub_le_of_dist_bdd {p : ℝ≥0∞} (hp' : p ≠ ∞) {s : Set α} (hs : measurable_set[m] s)
     {f g : α → β} {c : ℝ} (hc : 0 ≤ c) (hf : ∀ x ∈ s, dist (f x) (g x) ≤ c) :
-    snorm (s.indicator (f - g)) p μ ≤ Ennreal.ofReal c * μ s ^ (1 / p.toReal) :=
+    snorm (s.indicator (f - g)) p μ ≤ ENNReal.ofReal c * μ s ^ (1 / p.toReal) :=
   by
   by_cases hp : p = 0
   · simp [hp]
@@ -517,7 +517,7 @@ theorem snorm_sub_le_of_dist_bdd {p : ℝ≥0∞} (hp' : p ≠ ∞) {s : Set α}
     · simp [indicator_of_not_mem hx]
   refine' le_trans (snorm_mono this) _
   rw [snorm_indicator_const hs hp hp']
-  refine' Ennreal.mul_le_mul (le_of_eq _) le_rfl
+  refine' ENNReal.mul_le_mul (le_of_eq _) le_rfl
   rw [← ofReal_norm_eq_coe_nnnorm, Real.norm_eq_abs, abs_of_nonneg hc]
 #align measure_theory.snorm_sub_le_of_dist_bdd MeasureTheory.snorm_sub_le_of_dist_bdd
 
@@ -528,7 +528,7 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp
     (hfg : ∀ᵐ x ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))) :
     Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0) :=
   by
-  rw [Ennreal.tendsto_atTop_zero]
+  rw [ENNReal.tendsto_atTop_zero]
   intro ε hε
   by_cases ε < ∞
   swap
@@ -537,10 +537,10 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp
   by_cases hμ : μ = 0
   · exact ⟨0, fun n hn => by simp [hμ]⟩
   have hε' : 0 < ε.to_real / 3 :=
-    div_pos (Ennreal.toReal_pos (gt_iff_lt.1 hε).Ne.symm h.ne) (by norm_num)
+    div_pos (ENNReal.toReal_pos (gt_iff_lt.1 hε).Ne.symm h.ne) (by norm_num)
   have hdivp : 0 ≤ 1 / p.to_real := by
     refine' one_div_nonneg.2 _
-    rw [← Ennreal.zero_toReal, Ennreal.toReal_le_toReal Ennreal.zero_ne_top hp']
+    rw [← ENNReal.zero_toReal, ENNReal.toReal_le_toReal ENNReal.zero_ne_top hp']
     exact le_trans ennreal.zero_lt_one.le hp
   have hpow : 0 < measure_univ_nnreal μ ^ (1 / p.to_real) :=
     Real.rpow_pos_of_pos (measure_univ_nnreal_pos hμ) _
@@ -550,7 +550,7 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp
   rw [Metric.tendstoUniformlyOn_iff] at ht₂
   specialize
     ht₂ (ε.to_real / (3 * measure_univ_nnreal μ ^ (1 / p.to_real)))
-      (div_pos (Ennreal.toReal_pos (gt_iff_lt.1 hε).Ne.symm h.ne) (mul_pos (by norm_num) hpow))
+      (div_pos (ENNReal.toReal_pos (gt_iff_lt.1 hε).Ne.symm h.ne) (mul_pos (by norm_num) hpow))
   obtain ⟨N, hN⟩ := eventually_at_top.1 ht₂
   clear ht₂
   refine' ⟨N, fun n hn => _⟩
@@ -568,17 +568,17 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp
           (hg.indicator htm).neg.AeStronglyMeasurable hp)
         _)
       _
-  have hnf : snorm (t.indicator (f n)) p μ ≤ Ennreal.ofReal (ε.to_real / 3) :=
+  have hnf : snorm (t.indicator (f n)) p μ ≤ ENNReal.ofReal (ε.to_real / 3) :=
     by
     refine' hsnorm₁ n t htm (le_trans ht₁ _)
-    rw [Ennreal.ofReal_le_ofReal_iff hδ₁.le]
+    rw [ENNReal.ofReal_le_ofReal_iff hδ₁.le]
     exact min_le_left _ _
-  have hng : snorm (t.indicator g) p μ ≤ Ennreal.ofReal (ε.to_real / 3) :=
+  have hng : snorm (t.indicator g) p μ ≤ ENNReal.ofReal (ε.to_real / 3) :=
     by
     refine' hsnorm₂ t htm (le_trans ht₁ _)
-    rw [Ennreal.ofReal_le_ofReal_iff hδ₂.le]
+    rw [ENNReal.ofReal_le_ofReal_iff hδ₂.le]
     exact min_le_right _ _
-  have hlt : snorm (tᶜ.indicator (f n - g)) p μ ≤ Ennreal.ofReal (ε.to_real / 3) :=
+  have hlt : snorm (tᶜ.indicator (f n - g)) p μ ≤ ENNReal.ofReal (ε.to_real / 3) :=
     by
     specialize hN n hn
     have :=
@@ -586,25 +586,25 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp
         (dist_comm (g x) (f n x) ▸ (hN x hx).le :
           dist (f n x) (g x) ≤ ε.to_real / (3 * measure_univ_nnreal μ ^ (1 / p.to_real)))
     refine' le_trans this _
-    rw [div_mul_eq_div_mul_one_div, ← Ennreal.ofReal_toReal (measure_lt_top μ (tᶜ)).Ne,
-      Ennreal.ofReal_rpow_of_nonneg Ennreal.toReal_nonneg hdivp, ← Ennreal.ofReal_mul, mul_assoc]
-    · refine' Ennreal.ofReal_le_ofReal (mul_le_of_le_one_right hε'.le _)
+    rw [div_mul_eq_div_mul_one_div, ← ENNReal.ofReal_toReal (measure_lt_top μ (tᶜ)).Ne,
+      ENNReal.ofReal_rpow_of_nonneg ENNReal.toReal_nonneg hdivp, ← ENNReal.ofReal_mul, mul_assoc]
+    · refine' ENNReal.ofReal_le_ofReal (mul_le_of_le_one_right hε'.le _)
       rw [mul_comm, mul_one_div, div_le_one]
       · refine'
-          Real.rpow_le_rpow Ennreal.toReal_nonneg
-            (Ennreal.toReal_le_of_le_ofReal (measure_univ_nnreal_pos hμ).le _) hdivp
-        rw [Ennreal.ofReal_coe_nNReal, coe_measure_univ_nnreal]
+          Real.rpow_le_rpow ENNReal.toReal_nonneg
+            (ENNReal.toReal_le_of_le_ofReal (measure_univ_nnreal_pos hμ).le _) hdivp
+        rw [ENNReal.ofReal_coe_nnreal, coe_measure_univ_nnreal]
         exact measure_mono (subset_univ _)
       · exact Real.rpow_pos_of_pos (measure_univ_nnreal_pos hμ) _
     · refine' mul_nonneg hε'.le (one_div_nonneg.2 hpow.le)
     · rw [div_mul_eq_div_mul_one_div]
       exact mul_nonneg hε'.le (one_div_nonneg.2 hpow.le)
-  have : Ennreal.ofReal (ε.to_real / 3) = ε / 3 :=
+  have : ENNReal.ofReal (ε.to_real / 3) = ε / 3 :=
     by
-    rw [Ennreal.ofReal_div_of_pos (show (0 : ℝ) < 3 by norm_num), Ennreal.ofReal_toReal h.ne]
+    rw [ENNReal.ofReal_div_of_pos (show (0 : ℝ) < 3 by norm_num), ENNReal.ofReal_toReal h.ne]
     simp
   rw [this] at hnf hng hlt
-  rw [snorm_neg, ← Ennreal.add_thirds ε, ← sub_eq_add_neg]
+  rw [snorm_neg, ← ENNReal.add_thirds ε, ← sub_eq_add_neg]
   exact add_le_add_three hnf hng hlt
 #align measure_theory.tendsto_Lp_of_tendsto_ae_of_meas MeasureTheory.tendsto_Lp_of_tendsto_ae_of_meas
 
@@ -638,8 +638,8 @@ theorem unifIntegrableOfTendstoLpZero (hp : 1 ≤ p) (hp' : p ≠ ∞) (hf : ∀
     (hf_tendsto : Tendsto (fun n => snorm (f n) p μ) atTop (𝓝 0)) : UnifIntegrable f p μ :=
   by
   intro ε hε
-  rw [Ennreal.tendsto_atTop_zero] at hf_tendsto
-  obtain ⟨N, hN⟩ := hf_tendsto (Ennreal.ofReal ε) (by simpa)
+  rw [ENNReal.tendsto_atTop_zero] at hf_tendsto
+  obtain ⟨N, hN⟩ := hf_tendsto (ENNReal.ofReal ε) (by simpa)
   set F : Fin N → α → β := fun n => f n
   have hF : ∀ n, mem_ℒp (F n) p μ := fun n => hf n
   obtain ⟨δ₁, hδpos₁, hδ₁⟩ := unif_integrable_fin μ hp hp' hF hε
@@ -691,7 +691,7 @@ theorem tendstoInMeasure_iff_tendsto_Lp [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp'
     TendstoInMeasure μ f atTop g ∧ UnifIntegrable f p μ ↔
       Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0) :=
   ⟨fun h => tendsto_Lp_of_tendstoInMeasure μ hp hp' (fun n => (hf n).1) hg h.2 h.1, fun h =>
-    ⟨tendstoInMeasureOfTendstoSnorm (lt_of_lt_of_le Ennreal.zero_lt_one hp).Ne.symm
+    ⟨tendstoInMeasureOfTendstoSnorm (lt_of_lt_of_le ENNReal.zero_lt_one hp).Ne.symm
         (fun n => (hf n).AeStronglyMeasurable) hg.AeStronglyMeasurable h,
       unifIntegrableOfTendstoLp μ hp hp' hf hg h⟩⟩
 #align measure_theory.tendsto_in_measure_iff_tendsto_Lp MeasureTheory.tendstoInMeasure_iff_tendsto_Lp
@@ -703,17 +703,17 @@ theorem unifIntegrableOf' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β
       ∀ ε : ℝ,
         0 < ε →
           ∃ C : ℝ≥0,
-            0 < C ∧ ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ Ennreal.ofReal ε) :
+            0 < C ∧ ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε) :
     UnifIntegrable f p μ :=
   by
-  have hpzero := (lt_of_lt_of_le Ennreal.zero_lt_one hp).Ne.symm
+  have hpzero := (lt_of_lt_of_le ENNReal.zero_lt_one hp).Ne.symm
   by_cases hμ : μ Set.univ = 0
   · rw [measure.measure_univ_eq_zero] at hμ
     exact hμ.symm ▸ unif_integrable_zero_meas
   intro ε hε
   obtain ⟨C, hCpos, hC⟩ := h (ε / 2) (half_pos hε)
   refine'
-    ⟨(ε / (2 * C)) ^ Ennreal.toReal p,
+    ⟨(ε / (2 * C)) ^ ENNReal.toReal p,
       Real.rpow_pos_of_pos (div_pos hε (mul_pos two_pos (NNReal.coe_pos.2 hCpos))) _,
       fun i s hs hμs => _⟩
   by_cases hμs' : μ s = 0
@@ -751,7 +751,7 @@ theorem unifIntegrableOf' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β
         rw [disjoint_iff_inf_le]
         rintro x ⟨hx₁ : _ ≤ _, hx₂ : _ < _⟩
         exact False.elim (hx₂.ne (eq_of_le_of_not_lt hx₁ (not_lt.2 hx₂.le)).symm)
-    _ ≤ snorm (indicator { x | C ≤ ‖f i x‖₊ } (f i)) p μ + C * μ s ^ (1 / Ennreal.toReal p) :=
+    _ ≤ snorm (indicator { x | C ≤ ‖f i x‖₊ } (f i)) p μ + C * μ s ^ (1 / ENNReal.toReal p) :=
       by
       refine'
         add_le_add (snorm_mono fun x => norm_indicator_le_of_subset (inter_subset_right _ _) _ _) _
@@ -763,22 +763,22 @@ theorem unifIntegrableOf' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β
         simp_rw [norm_indicator_eq_indicator_norm]
         exact indicator_le' (fun x (hx : _ < _) => hx.le) fun _ _ => NNReal.coe_nonneg _
       refine' le_trans (snorm_le_of_ae_bound this) _
-      rw [mul_comm, measure.restrict_apply' hs, univ_inter, Ennreal.ofReal_coe_nNReal, one_div]
+      rw [mul_comm, measure.restrict_apply' hs, univ_inter, ENNReal.ofReal_coe_nnreal, one_div]
       exacts[le_rfl, hs]
-    _ ≤ Ennreal.ofReal (ε / 2) + C * Ennreal.ofReal (ε / (2 * C)) :=
+    _ ≤ ENNReal.ofReal (ε / 2) + C * ENNReal.ofReal (ε / (2 * C)) :=
       by
       refine' add_le_add (hC i) (mul_le_mul_left' _ _)
-      rwa [Ennreal.rpow_one_div_le_iff (Ennreal.toReal_pos hpzero hp'),
-        Ennreal.ofReal_rpow_of_pos (div_pos hε (mul_pos two_pos (NNReal.coe_pos.2 hCpos)))]
-    _ ≤ Ennreal.ofReal (ε / 2) + Ennreal.ofReal (ε / 2) :=
+      rwa [ENNReal.rpow_one_div_le_iff (ENNReal.toReal_pos hpzero hp'),
+        ENNReal.ofReal_rpow_of_pos (div_pos hε (mul_pos two_pos (NNReal.coe_pos.2 hCpos)))]
+    _ ≤ ENNReal.ofReal (ε / 2) + ENNReal.ofReal (ε / 2) :=
       by
       refine' add_le_add_left _ _
-      rw [← Ennreal.ofReal_coe_nNReal, ← Ennreal.ofReal_mul (NNReal.coe_nonneg _), ← div_div,
+      rw [← ENNReal.ofReal_coe_nnreal, ← ENNReal.ofReal_mul (NNReal.coe_nonneg _), ← div_div,
         mul_div_cancel' _ (NNReal.coe_pos.2 hCpos).Ne.symm]
       exact le_rfl
-    _ ≤ Ennreal.ofReal ε :=
+    _ ≤ ENNReal.ofReal ε :=
       by
-      rw [← Ennreal.ofReal_add (half_pos hε).le (half_pos hε).le, add_halves]
+      rw [← ENNReal.ofReal_add (half_pos hε).le (half_pos hε).le, add_halves]
       exact le_rfl
     
 #align measure_theory.unif_integrable_of' MeasureTheory.unifIntegrableOf'
@@ -788,14 +788,14 @@ theorem unifIntegrableOf (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β}
     (h :
       ∀ ε : ℝ,
         0 < ε →
-          ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ Ennreal.ofReal ε) :
+          ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε) :
     UnifIntegrable f p μ := by
   set g : ι → α → β := fun i => (hf i).some
   refine'
     (unif_integrable_of' μ hp hp' (fun i => (Exists.choose_spec <| hf i).1) fun ε hε => _).ae_eq
       fun i => (Exists.choose_spec <| hf i).2.symm
   obtain ⟨C, hC⟩ := h ε hε
-  have hCg : ∀ i, snorm ({ x | C ≤ ‖g i x‖₊ }.indicator (g i)) p μ ≤ Ennreal.ofReal ε :=
+  have hCg : ∀ i, snorm ({ x | C ≤ ‖g i x‖₊ }.indicator (g i)) p μ ≤ ENNReal.ofReal ε :=
     by
     intro i
     refine' le_trans (le_of_eq <| snorm_congr_ae _) (hC i)
@@ -860,7 +860,7 @@ theorem uniformIntegrableFinite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠ 
       (finset.univ.image fun i : ι => snorm (f i) p μ).max'
         ⟨snorm (f hι.some) p μ, Finset.mem_image.2 ⟨hι.some, Finset.mem_univ _, rfl⟩⟩
     refine' ⟨C.to_nnreal, fun i => _⟩
-    rw [Ennreal.coe_toNnreal]
+    rw [ENNReal.coe_toNNReal]
     · exact Finset.le_max' _ _ (Finset.mem_image.2 ⟨i, Finset.mem_univ _, rfl⟩)
     · refine' ne_of_lt ((Finset.max'_lt_iff _ _).2 fun y hy => _)
       rw [Finset.mem_image] at hy
@@ -879,7 +879,7 @@ theorem uniformIntegrableSubsingleton [Subsingleton ι] (hp_one : 1 ≤ p) (hp_t
 theorem uniformIntegrableConst {g : α → β} (hp : 1 ≤ p) (hp_ne_top : p ≠ ∞) (hg : Memℒp g p μ) :
     UniformIntegrable (fun n : ι => g) p μ :=
   ⟨fun i => hg.1, unifIntegrableConst μ hp hp_ne_top hg,
-    ⟨(snorm g p μ).toNNReal, fun i => le_of_eq (Ennreal.coe_toNnreal hg.2.Ne).symm⟩⟩
+    ⟨(snorm g p μ).toNNReal, fun i => le_of_eq (ENNReal.coe_toNNReal hg.2.Ne).symm⟩⟩
 #align measure_theory.uniform_integrable_const MeasureTheory.uniformIntegrableConst
 
 /-- This lemma is superceded by `uniform_integrable_of` which only requires
@@ -889,7 +889,7 @@ theorem uniformIntegrableOf' [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ 
     (h :
       ∀ ε : ℝ,
         0 < ε →
-          ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ Ennreal.ofReal ε) :
+          ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε) :
     UniformIntegrable f p μ :=
   by
   refine'
@@ -923,18 +923,18 @@ theorem uniformIntegrableOf' [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ 
         refine' eventually_of_forall _
         simp_rw [nnnorm_indicator_eq_indicator_nnnorm]
         exact indicator_le fun x (hx : _ < _) => hx.le
-      refine' add_le_add (le_trans (snorm_le_of_ae_bound this) _) (Ennreal.ofReal_one ▸ hC i)
-      rw [Ennreal.ofReal_coe_nNReal, mul_comm]
+      refine' add_le_add (le_trans (snorm_le_of_ae_bound this) _) (ENNReal.ofReal_one ▸ hC i)
+      rw [ENNReal.ofReal_coe_nnreal, mul_comm]
       exact le_rfl
     _ = (C * μ univ ^ p.to_real⁻¹ + 1 : ℝ≥0∞).toNNReal :=
       by
-      rw [Ennreal.coe_toNnreal]
+      rw [ENNReal.coe_toNNReal]
       exact
-        Ennreal.add_ne_top.2
-          ⟨Ennreal.mul_ne_top Ennreal.coe_ne_top
-              (Ennreal.rpow_ne_top_of_nonneg (inv_nonneg.2 Ennreal.toReal_nonneg)
+        ENNReal.add_ne_top.2
+          ⟨ENNReal.mul_ne_top ENNReal.coe_ne_top
+              (ENNReal.rpow_ne_top_of_nonneg (inv_nonneg.2 ENNReal.toReal_nonneg)
                 (measure_lt_top _ _).Ne),
-            Ennreal.one_ne_top⟩
+            ENNReal.one_ne_top⟩
     
 #align measure_theory.uniform_integrable_of' MeasureTheory.uniformIntegrableOf'
 
@@ -945,7 +945,7 @@ theorem uniformIntegrableOf [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞
     (h :
       ∀ ε : ℝ,
         0 < ε →
-          ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ Ennreal.ofReal ε) :
+          ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε) :
     UniformIntegrable f p μ :=
   by
   set g : ι → α → β := fun i => (hf i).some
@@ -965,11 +965,11 @@ theorem uniformIntegrableOf [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞
 /-- This lemma is superceded by `uniform_integrable.spec` which does not require measurability. -/
 theorem UniformIntegrable.spec' (hp : p ≠ 0) (hp' : p ≠ ∞) (hf : ∀ i, StronglyMeasurable (f i))
     (hfu : UniformIntegrable f p μ) {ε : ℝ} (hε : 0 < ε) :
-    ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ Ennreal.ofReal ε :=
+    ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε :=
   by
   obtain ⟨-, hfu, M, hM⟩ := hfu
   obtain ⟨δ, hδpos, hδ⟩ := hfu hε
-  obtain ⟨C, hC⟩ : ∃ C : ℝ≥0, ∀ i, μ { x | C ≤ ‖f i x‖₊ } ≤ Ennreal.ofReal δ :=
+  obtain ⟨C, hC⟩ : ∃ C : ℝ≥0, ∀ i, μ { x | C ≤ ‖f i x‖₊ } ≤ ENNReal.ofReal δ :=
     by
     by_contra hcon
     push_neg  at hcon
@@ -981,11 +981,11 @@ theorem UniformIntegrable.spec' (hp : p ≠ 0) (hp' : p ≠ ∞) (hf : ∀ i, St
       calc
         C • (δ : ℝ≥0∞) ^ (1 / p.to_real) ≤ C • μ { x | C ≤ ‖f (ℐ C) x‖₊ } ^ (1 / p.to_real) :=
           by
-          rw [Ennreal.smul_def, Ennreal.smul_def, smul_eq_mul, smul_eq_mul]
-          simp_rw [Ennreal.ofReal_coe_nNReal] at hℐ
+          rw [ENNReal.smul_def, ENNReal.smul_def, smul_eq_mul, smul_eq_mul]
+          simp_rw [ENNReal.ofReal_coe_nnreal] at hℐ
           refine'
-            Ennreal.mul_le_mul le_rfl
-              (Ennreal.rpow_le_rpow (hℐ C).le (one_div_nonneg.2 Ennreal.toReal_nonneg))
+            ENNReal.mul_le_mul le_rfl
+              (ENNReal.rpow_le_rpow (hℐ C).le (one_div_nonneg.2 ENNReal.toReal_nonneg))
         _ ≤ snorm ({ x | C ≤ ‖f (ℐ C) x‖₊ }.indicator (f (ℐ C))) p μ :=
           by
           refine'
@@ -996,22 +996,22 @@ theorem UniformIntegrable.spec' (hp : p ≠ 0) (hp' : p ≠ ∞) (hf : ∀ i, St
         _ ≤ snorm (f (ℐ C)) p μ := snorm_indicator_le _
         
     specialize this (2 * max M 1 * δ⁻¹ ^ (1 / p.to_real))
-    rw [Ennreal.coe_rpow_of_nonneg _ (one_div_nonneg.2 Ennreal.toReal_nonneg), ← Ennreal.coe_smul,
+    rw [ENNReal.coe_rpow_of_nonneg _ (one_div_nonneg.2 ENNReal.toReal_nonneg), ← ENNReal.coe_smul,
       smul_eq_mul, mul_assoc, NNReal.inv_rpow,
-      inv_mul_cancel (NNReal.rpow_pos (NNReal.coe_pos.1 hδpos)).Ne.symm, mul_one, Ennreal.coe_mul, ←
+      inv_mul_cancel (NNReal.rpow_pos (NNReal.coe_pos.1 hδpos)).Ne.symm, mul_one, ENNReal.coe_mul, ←
       NNReal.inv_rpow] at this
     refine'
       (lt_of_le_of_lt (le_trans (hM <| ℐ <| 2 * max M 1 * δ⁻¹ ^ (1 / p.to_real)) (le_max_left M 1))
             (lt_of_lt_of_le _ this)).Ne
         rfl
-    rw [← Ennreal.coe_one, ← WithTop.coe_max, ← Ennreal.coe_mul, Ennreal.coe_lt_coe]
+    rw [← ENNReal.coe_one, ← WithTop.coe_max, ← ENNReal.coe_mul, ENNReal.coe_lt_coe]
     exact lt_two_mul_self (lt_max_of_lt_right one_pos)
   exact ⟨C, fun i => hδ i _ (measurableSet_le measurable_const (hf i).nnnorm.Measurable) (hC i)⟩
 #align measure_theory.uniform_integrable.spec' MeasureTheory.UniformIntegrable.spec'
 
 theorem UniformIntegrable.spec (hp : p ≠ 0) (hp' : p ≠ ∞) (hfu : UniformIntegrable f p μ) {ε : ℝ}
     (hε : 0 < ε) :
-    ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ Ennreal.ofReal ε :=
+    ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε :=
   by
   set g : ι → α → β := fun i => (hfu.1 i).some
   have hgmeas : ∀ i, strongly_measurable (g i) := fun i => (Exists.choose_spec <| hfu.1 i).1
@@ -1033,8 +1033,8 @@ theorem uniformIntegrable_iff [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ 
       (∀ i, AeStronglyMeasurable (f i) μ) ∧
         ∀ ε : ℝ,
           0 < ε →
-            ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ Ennreal.ofReal ε :=
-  ⟨fun h => ⟨h.1, fun ε => h.spec (lt_of_lt_of_le Ennreal.zero_lt_one hp).Ne.symm hp'⟩, fun h =>
+            ∃ C : ℝ≥0, ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε :=
+  ⟨fun h => ⟨h.1, fun ε => h.spec (lt_of_lt_of_le ENNReal.zero_lt_one hp).Ne.symm hp'⟩, fun h =>
     uniformIntegrableOf hp hp' h.1 h.2⟩
 #align measure_theory.uniform_integrable_iff MeasureTheory.uniformIntegrable_iff
 
@@ -1062,13 +1062,13 @@ theorem uniformIntegrableAverage (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf : U
     simp_rw [this, snorm_const_smul, ← Finset.mul_sum, nnnorm_inv, Real.nnnorm_coe_nat]
     by_cases hn : (↑(↑n : ℝ≥0)⁻¹ : ℝ≥0∞) = 0
     · simp only [hn, zero_mul, zero_le]
-    refine' le_trans _ (_ : ↑(↑n : ℝ≥0)⁻¹ * n • Ennreal.ofReal ε ≤ Ennreal.ofReal ε)
-    · refine' (Ennreal.mul_le_mul_left hn Ennreal.coe_ne_top).2 _
+    refine' le_trans _ (_ : ↑(↑n : ℝ≥0)⁻¹ * n • ENNReal.ofReal ε ≤ ENNReal.ofReal ε)
+    · refine' (ENNReal.mul_le_mul_left hn ENNReal.coe_ne_top).2 _
       conv_rhs => rw [← Finset.card_range n]
       exact Finset.sum_le_card_nsmul _ _ _ fun i hi => hδ₂ _ _ hs hle
-    · simp only [Ennreal.coe_eq_zero, inv_eq_zero, Nat.cast_eq_zero] at hn
-      rw [nsmul_eq_mul, ← mul_assoc, Ennreal.coe_inv, Ennreal.coe_nat,
-        Ennreal.inv_mul_cancel _ (Ennreal.nat_ne_top _), one_mul]
+    · simp only [ENNReal.coe_eq_zero, inv_eq_zero, Nat.cast_eq_zero] at hn
+      rw [nsmul_eq_mul, ← mul_assoc, ENNReal.coe_inv, ENNReal.coe_nat,
+        ENNReal.inv_mul_cancel _ (ENNReal.nat_ne_top _), one_mul]
       · exact le_rfl
       all_goals simpa only [Ne.def, Nat.cast_eq_zero]
   · obtain ⟨C, hC⟩ := hf₃
@@ -1083,12 +1083,12 @@ theorem uniformIntegrableAverage (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf : U
     by_cases hn : (↑(↑n : ℝ≥0)⁻¹ : ℝ≥0∞) = 0
     · simp only [hn, zero_mul, zero_le]
     refine' le_trans _ (_ : ↑(↑n : ℝ≥0)⁻¹ * (n • C : ℝ≥0∞) ≤ C)
-    · refine' (Ennreal.mul_le_mul_left hn Ennreal.coe_ne_top).2 _
+    · refine' (ENNReal.mul_le_mul_left hn ENNReal.coe_ne_top).2 _
       conv_rhs => rw [← Finset.card_range n]
       exact Finset.sum_le_card_nsmul _ _ _ fun i hi => hC i
-    · simp only [Ennreal.coe_eq_zero, inv_eq_zero, Nat.cast_eq_zero] at hn
-      rw [nsmul_eq_mul, ← mul_assoc, Ennreal.coe_inv, Ennreal.coe_nat,
-        Ennreal.inv_mul_cancel _ (Ennreal.nat_ne_top _), one_mul]
+    · simp only [ENNReal.coe_eq_zero, inv_eq_zero, Nat.cast_eq_zero] at hn
+      rw [nsmul_eq_mul, ← mul_assoc, ENNReal.coe_inv, ENNReal.coe_nat,
+        ENNReal.inv_mul_cancel _ (ENNReal.nat_ne_top _), one_mul]
       · exact le_rfl
       all_goals simpa only [Ne.def, Nat.cast_eq_zero]
 #align measure_theory.uniform_integrable_average MeasureTheory.uniformIntegrableAverage

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

A PR analogous to #12338: reformatting proofs following the multiple goals linter of #12339.

@@ -234,23 +234,23 @@ theorem Memℒp.snormEssSup_indicator_norm_ge_eq_zero (hf : Memℒp f ∞ μ)
   have hbdd : snormEssSup f μ < ∞ := hf.snorm_lt_top
   refine' ⟨(snorm f ∞ μ + 1).toReal, _⟩
   rw [snormEssSup_indicator_eq_snormEssSup_restrict]
-  have : μ.restrict { x : α | (snorm f ⊤ μ + 1).toReal ≤ ‖f x‖₊ } = 0 := by
-    simp only [coe_nnnorm, snorm_exponent_top, Measure.restrict_eq_zero]
-    have : { x : α | (snormEssSup f μ + 1).toReal ≤ ‖f x‖ } ⊆
-        { x : α | snormEssSup f μ < ‖f x‖₊ } := by
-      intro x hx
-      rw [Set.mem_setOf_eq, ← ENNReal.toReal_lt_toReal hbdd.ne ENNReal.coe_lt_top.ne,
-        ENNReal.coe_toReal, coe_nnnorm]
-      refine' lt_of_lt_of_le _ hx
-      rw [ENNReal.toReal_lt_toReal hbdd.ne]
-      · exact ENNReal.lt_add_right hbdd.ne one_ne_zero
-      · exact (ENNReal.add_lt_top.2 ⟨hbdd, ENNReal.one_lt_top⟩).ne
-    rw [← nonpos_iff_eq_zero]
-    refine' (measure_mono this).trans _
-    have hle := coe_nnnorm_ae_le_snormEssSup f μ
-    simp_rw [ae_iff, not_le] at hle
-    exact nonpos_iff_eq_zero.2 hle
-  rw [this, snormEssSup_measure_zero]
+  · have : μ.restrict { x : α | (snorm f ⊤ μ + 1).toReal ≤ ‖f x‖₊ } = 0 := by
+      simp only [coe_nnnorm, snorm_exponent_top, Measure.restrict_eq_zero]
+      have : { x : α | (snormEssSup f μ + 1).toReal ≤ ‖f x‖ } ⊆
+          { x : α | snormEssSup f μ < ‖f x‖₊ } := by
+        intro x hx
+        rw [Set.mem_setOf_eq, ← ENNReal.toReal_lt_toReal hbdd.ne ENNReal.coe_lt_top.ne,
+          ENNReal.coe_toReal, coe_nnnorm]
+        refine' lt_of_lt_of_le _ hx
+        rw [ENNReal.toReal_lt_toReal hbdd.ne]
+        · exact ENNReal.lt_add_right hbdd.ne one_ne_zero
+        · exact (ENNReal.add_lt_top.2 ⟨hbdd, ENNReal.one_lt_top⟩).ne
+      rw [← nonpos_iff_eq_zero]
+      refine' (measure_mono this).trans _
+      have hle := coe_nnnorm_ae_le_snormEssSup f μ
+      simp_rw [ae_iff, not_le] at hle
+      exact nonpos_iff_eq_zero.2 hle
+    rw [this, snormEssSup_measure_zero]
   exact measurableSet_le measurable_const hmeas.nnnorm.measurable.subtype_coe
 #align measure_theory.mem_ℒp.snorm_ess_sup_indicator_norm_ge_eq_zero MeasureTheory.Memℒp.snormEssSup_indicator_norm_ge_eq_zero
 
@@ -284,7 +284,8 @@ theorem Memℒp.snorm_indicator_norm_ge_le (hf : Memℒp f p μ) (hmeas : Strong
         (one_div_pos.2 <| ENNReal.toReal_pos hp_ne_zero hp_ne_top), ← Real.rpow_mul (norm_nonneg _),
       mul_one_div_cancel (ENNReal.toReal_pos hp_ne_zero hp_ne_top).ne.symm, Real.rpow_one]
   by_cases hx : x ∈ { x : α | M ^ (1 / p.toReal) ≤ ‖f x‖₊ }
-  · rw [Set.indicator_of_mem hx, Set.indicator_of_mem, Real.nnnorm_of_nonneg]; rfl
+  · rw [Set.indicator_of_mem hx, Set.indicator_of_mem, Real.nnnorm_of_nonneg]
+    · rfl
     rw [Set.mem_setOf_eq]
     rwa [← hiff]
   · rw [Set.indicator_of_not_mem hx, Set.indicator_of_not_mem]
@@ -351,8 +352,8 @@ theorem Memℒp.snorm_indicator_le' (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) (hf
     snorm_indicator_le_of_bound (f := { x | ‖f x‖ < M }.indicator f) hp_top hε (by
       intro x
       rw [norm_indicator_eq_indicator_norm, Set.indicator_apply]
-      split_ifs with h
-      exacts [h, hMpos])
+      · split_ifs with h
+        exacts [h, hMpos])
   · refine' ⟨δ, hδpos, fun s hs hμs => _⟩
     rw [(_ : f = { x : α | M ≤ ‖f x‖₊ }.indicator f + { x : α | ‖f x‖ < M }.indicator f)]
     · rw [snorm_indicator_eq_snorm_restrict hs]

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -443,8 +443,7 @@ theorem unifIntegrable_fin (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) {n : ℕ} {f
     · have hi' := Fin.is_lt i
       rw [Nat.lt_succ_iff] at hi'
       rw [not_lt] at hi
-      -- Porting note: Original proof was `simp [← le_antisymm hi' hi]`
-      ext; symm; rw [Fin.coe_ofNat_eq_mod, le_antisymm hi' hi, Nat.mod_succ_eq_iff_lt, Nat.lt_succ]
+      simp [← le_antisymm hi' hi]
 #align measure_theory.unif_integrable_fin MeasureTheory.unifIntegrable_fin
 
 /-- A finite sequence of Lp functions is uniformly integrable. -/

This is less exhaustive than its sibling #11486 because edge cases are harder to classify. No fundamental difficulty, just me being a bit fast and lazy.

Reduce the diff of #11203

@@ -929,7 +929,7 @@ theorem uniformIntegrable_average
     refine' le_trans (snorm_sum_le (fun i _ => ((hf₁ i).const_smul _).indicator hs) hp) _
     have : ∀ i, s.indicator ((n : ℝ) ⁻¹ • f i) = (↑n : ℝ)⁻¹ • s.indicator (f i) :=
       fun i ↦ indicator_const_smul _ _ _
-    simp_rw [this, snorm_const_smul, ← Finset.mul_sum, nnnorm_inv, Real.nnnorm_coe_nat]
+    simp_rw [this, snorm_const_smul, ← Finset.mul_sum, nnnorm_inv, Real.nnnorm_natCast]
     by_cases hn : (↑(↑n : ℝ≥0)⁻¹ : ℝ≥0∞) = 0
     · simp only [hn, zero_mul, zero_le]
     refine' le_trans _ (_ : ↑(↑n : ℝ≥0)⁻¹ * n • ENNReal.ofReal ε ≤ ENNReal.ofReal ε)
@@ -937,13 +937,13 @@ theorem uniformIntegrable_average
       conv_rhs => rw [← Finset.card_range n]
       exact Finset.sum_le_card_nsmul _ _ _ fun i _ => hδ₂ _ _ hs hle
     · simp only [ENNReal.coe_eq_zero, inv_eq_zero, Nat.cast_eq_zero] at hn
-      rw [nsmul_eq_mul, ← mul_assoc, ENNReal.coe_inv, ENNReal.coe_nat,
-        ENNReal.inv_mul_cancel _ (ENNReal.nat_ne_top _), one_mul]
+      rw [nsmul_eq_mul, ← mul_assoc, ENNReal.coe_inv, ENNReal.coe_natCast,
+        ENNReal.inv_mul_cancel _ (ENNReal.natCast_ne_top _), one_mul]
       all_goals simpa only [Ne, Nat.cast_eq_zero]
   · obtain ⟨C, hC⟩ := hf₃
     simp_rw [Finset.smul_sum]
     refine' ⟨C, fun n => (snorm_sum_le (fun i _ => (hf₁ i).const_smul _) hp).trans _⟩
-    simp_rw [snorm_const_smul, ← Finset.mul_sum, nnnorm_inv, Real.nnnorm_coe_nat]
+    simp_rw [snorm_const_smul, ← Finset.mul_sum, nnnorm_inv, Real.nnnorm_natCast]
     by_cases hn : (↑(↑n : ℝ≥0)⁻¹ : ℝ≥0∞) = 0
     · simp only [hn, zero_mul, zero_le]
     refine' le_trans _ (_ : ↑(↑n : ℝ≥0)⁻¹ * (n • C : ℝ≥0∞) ≤ C)
@@ -951,8 +951,8 @@ theorem uniformIntegrable_average
       conv_rhs => rw [← Finset.card_range n]
       exact Finset.sum_le_card_nsmul _ _ _ fun i _ => hC i
     · simp only [ENNReal.coe_eq_zero, inv_eq_zero, Nat.cast_eq_zero] at hn
-      rw [nsmul_eq_mul, ← mul_assoc, ENNReal.coe_inv, ENNReal.coe_nat,
-        ENNReal.inv_mul_cancel _ (ENNReal.nat_ne_top _), one_mul]
+      rw [nsmul_eq_mul, ← mul_assoc, ENNReal.coe_inv, ENNReal.coe_natCast,
+        ENNReal.inv_mul_cancel _ (ENNReal.natCast_ne_top _), one_mul]
       all_goals simpa only [Ne, Nat.cast_eq_zero]
 
 /-- The averaging of a uniformly integrable real-valued sequence is also uniformly integrable. -/

@@ -334,7 +334,7 @@ theorem snorm_indicator_le_of_bound {f : α → β} (hp_top : p ≠ ∞) {ε : 
     refine' le_trans hμ _
     rw [← ENNReal.ofReal_rpow_of_pos (div_pos hε hM),
       ENNReal.rpow_le_rpow_iff (ENNReal.toReal_pos hp hp_top), ENNReal.ofReal_div_of_pos hM]
-  · simpa only [ENNReal.ofReal_eq_zero, not_le, Ne.def]
+  · simpa only [ENNReal.ofReal_eq_zero, not_le, Ne]
 #align measure_theory.snorm_indicator_le_of_bound MeasureTheory.snorm_indicator_le_of_bound
 
 section
@@ -939,7 +939,7 @@ theorem uniformIntegrable_average
     · simp only [ENNReal.coe_eq_zero, inv_eq_zero, Nat.cast_eq_zero] at hn
       rw [nsmul_eq_mul, ← mul_assoc, ENNReal.coe_inv, ENNReal.coe_nat,
         ENNReal.inv_mul_cancel _ (ENNReal.nat_ne_top _), one_mul]
-      all_goals simpa only [Ne.def, Nat.cast_eq_zero]
+      all_goals simpa only [Ne, Nat.cast_eq_zero]
   · obtain ⟨C, hC⟩ := hf₃
     simp_rw [Finset.smul_sum]
     refine' ⟨C, fun n => (snorm_sum_le (fun i _ => (hf₁ i).const_smul _) hp).trans _⟩
@@ -953,7 +953,7 @@ theorem uniformIntegrable_average
     · simp only [ENNReal.coe_eq_zero, inv_eq_zero, Nat.cast_eq_zero] at hn
       rw [nsmul_eq_mul, ← mul_assoc, ENNReal.coe_inv, ENNReal.coe_nat,
         ENNReal.inv_mul_cancel _ (ENNReal.nat_ne_top _), one_mul]
-      all_goals simpa only [Ne.def, Nat.cast_eq_zero]
+      all_goals simpa only [Ne, Nat.cast_eq_zero]
 
 /-- The averaging of a uniformly integrable real-valued sequence is also uniformly integrable. -/
 theorem uniformIntegrable_average_real (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf : UniformIntegrable f p μ) :

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

| Statement | New name | Old name | |

@@ -691,7 +691,7 @@ theorem unifIntegrable_of' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → 
     _ ≤ ENNReal.ofReal (ε / 2) + ENNReal.ofReal (ε / 2) := by
       refine' add_le_add_left _ _
       rw [← ENNReal.ofReal_coe_nnreal, ← ENNReal.ofReal_mul (NNReal.coe_nonneg _), ← div_div,
-        mul_div_cancel' _ (NNReal.coe_pos.2 hCpos).ne.symm]
+        mul_div_cancel₀ _ (NNReal.coe_pos.2 hCpos).ne.symm]
     _ ≤ ENNReal.ofReal ε := by
       rw [← ENNReal.ofReal_add (half_pos hε).le (half_pos hε).le, add_halves]
 #align measure_theory.unif_integrable_of' MeasureTheory.unifIntegrable_of'

This is presumably not exhaustive, but covers about a hundred instances.

Style opinions (e.g., why a particular change is great/not a good idea) are very welcome; I'm still forming my own.

@@ -679,7 +679,7 @@ theorem unifIntegrable_of' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → 
       rw [← Set.indicator_indicator]
       rw [snorm_indicator_eq_snorm_restrict hs]
       have : ∀ᵐ x ∂μ.restrict s, ‖{ x : α | ‖f i x‖₊ < C }.indicator (f i) x‖ ≤ C := by
-        refine' ae_of_all _ _
+        filter_upwards
         simp_rw [norm_indicator_eq_indicator_norm]
         exact Set.indicator_le' (fun x (hx : _ < _) => hx.le) fun _ _ => NNReal.coe_nonneg _
       refine' le_trans (snorm_le_of_ae_bound this) _
@@ -816,7 +816,7 @@ theorem uniformIntegrable_of' [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ 
           simpa using hx
     _ ≤ (C : ℝ≥0∞) * μ Set.univ ^ p.toReal⁻¹ + 1 := by
       have : ∀ᵐ x ∂μ, ‖{ x : α | ‖f i x‖₊ < C }.indicator (f i) x‖₊ ≤ C := by
-        refine' eventually_of_forall _
+        filter_upwards
         simp_rw [nnnorm_indicator_eq_indicator_nnnorm]
         exact Set.indicator_le fun x (hx : _ < _) => hx.le
       refine' add_le_add (le_trans (snorm_le_of_ae_bound this) _) (ENNReal.ofReal_one ▸ hC i)

I removed some of the tactics that were not used and are hopefully uncontroversial arising from the linter at #11308.

As the commit messages should convey, the removed tactics are, essentially,

push_cast
norm_cast
congr
norm_num
dsimp
funext
intro
infer_instance

@@ -664,8 +664,7 @@ theorem unifIntegrable_of' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → 
       change _ = fun x => (s ∩ { x : α | C ≤ ‖f i x‖₊ }).indicator (f i) x +
         (s ∩ { x : α | ‖f i x‖₊ < C }).indicator (f i) x
       rw [← Set.indicator_union_of_disjoint]
-      · congr
-        rw [← Set.inter_union_distrib_left, (by ext; simp [le_or_lt] :
+      · rw [← Set.inter_union_distrib_left, (by ext; simp [le_or_lt] :
             { x : α | C ≤ ‖f i x‖₊ } ∪ { x : α | ‖f i x‖₊ < C } = Set.univ),
           Set.inter_univ]
       · refine' (Disjoint.inf_right' _ _).inf_left' _

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -649,7 +649,7 @@ theorem unifIntegrable_of' (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → 
   by_cases hμs' : μ s = 0
   · rw [(snorm_eq_zero_iff ((hf i).indicator hs).aestronglyMeasurable hpzero).2
         (indicator_meas_zero hμs')]
-    norm_num
+    set_option tactic.skipAssignedInstances false in norm_num
   calc
     snorm (Set.indicator s (f i)) p μ ≤
         snorm (Set.indicator (s ∩ { x | C ≤ ‖f i x‖₊ }) (f i)) p μ +

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -437,7 +437,7 @@ theorem unifIntegrable_fin (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) {n : ℕ} {f
   by_cases hi : i.val < n
   · rw [(_ : f i = g ⟨i.val, hi⟩)]
     · exact hδ₁ _ s hs (le_trans hμs <| ENNReal.ofReal_le_ofReal <| min_le_left _ _)
-    · simp
+    · simp [g]
   · rw [(_ : i = n)]
     · exact hδ₂ _ hs (le_trans hμs <| ENNReal.ofReal_le_ofReal <| min_le_right _ _)
     · have hi' := Fin.is_lt i
@@ -457,7 +457,7 @@ theorem unifIntegrable_finite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞
   obtain ⟨δ, hδpos, hδ⟩ := unifIntegrable_fin hp_one hp_top hg hε
   refine' ⟨δ, hδpos, fun i s hs hμs => _⟩
   specialize hδ (hn.some i) s hs hμs
-  simp_rw [Function.comp_apply, Equiv.symm_apply_apply] at hδ
+  simp_rw [g, Function.comp_apply, Equiv.symm_apply_apply] at hδ
   assumption
 #align measure_theory.unif_integrable_finite MeasureTheory.unifIntegrable_finite
 

Classifies by adding issue number (#10754) to porting notes claiming added instance.

@@ -425,7 +425,8 @@ theorem unifIntegrable_fin (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) {n : ℕ} {f
   revert f
   induction' n with n h
   · intro f hf
-    have : Subsingleton (Fin Nat.zero) := subsingleton_fin_zero -- Porting note: Added this instance
+  -- Porting note (#10754): added this instance
+    have : Subsingleton (Fin Nat.zero) := subsingleton_fin_zero
     exact unifIntegrable_subsingleton hp_one hp_top hf
   intro f hfLp ε hε
   let g : Fin n → α → β := fun k => f k

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -395,7 +395,7 @@ theorem Memℒp.snorm_indicator_le (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) (hf :
   refine' ⟨δ, hδpos, fun s hs hμs => _⟩
   convert hδ s hs hμs using 1
   rw [snorm_indicator_eq_snorm_restrict hs, snorm_indicator_eq_snorm_restrict hs]
-  refine' snorm_congr_ae heq.restrict
+  exact snorm_congr_ae heq.restrict
 #align measure_theory.mem_ℒp.snorm_indicator_le MeasureTheory.Memℒp.snorm_indicator_le
 
 /-- A constant function is uniformly integrable. -/

A variable declaration made (μ) an explicit argument, even though it could be deduced from other arguments in almost all cases. The declaration was removed and the change propagated to other files.

@@ -165,7 +165,7 @@ theorem tendsto_indicator_ge (f : α → β) (x : α) :
   norm_cast
 #align measure_theory.tendsto_indicator_ge MeasureTheory.tendsto_indicator_ge
 
-variable (μ) {p : ℝ≥0∞}
+variable {p : ℝ≥0∞}
 
 section
 
@@ -213,7 +213,7 @@ which does not require measurability. -/
 theorem Memℒp.integral_indicator_norm_ge_nonneg_le_of_meas (hf : Memℒp f 1 μ)
     (hmeas : StronglyMeasurable f) {ε : ℝ} (hε : 0 < ε) :
     ∃ M : ℝ, 0 ≤ M ∧ (∫⁻ x, ‖{ x | M ≤ ‖f x‖₊ }.indicator f x‖₊ ∂μ) ≤ ENNReal.ofReal ε :=
-  let ⟨M, hM⟩ := hf.integral_indicator_norm_ge_le μ hmeas hε
+  let ⟨M, hM⟩ := hf.integral_indicator_norm_ge_le hmeas hε
   ⟨max M 0, le_max_right _ _, by simpa⟩
 #align measure_theory.mem_ℒp.integral_indicator_norm_ge_nonneg_le_of_meas MeasureTheory.Memℒp.integral_indicator_norm_ge_nonneg_le_of_meas
 
@@ -221,7 +221,7 @@ theorem Memℒp.integral_indicator_norm_ge_nonneg_le (hf : Memℒp f 1 μ) {ε :
     ∃ M : ℝ, 0 ≤ M ∧ (∫⁻ x, ‖{ x | M ≤ ‖f x‖₊ }.indicator f x‖₊ ∂μ) ≤ ENNReal.ofReal ε := by
   have hf_mk : Memℒp (hf.1.mk f) 1 μ := (memℒp_congr_ae hf.1.ae_eq_mk).mp hf
   obtain ⟨M, hM_pos, hfM⟩ :=
-    hf_mk.integral_indicator_norm_ge_nonneg_le_of_meas μ hf.1.stronglyMeasurable_mk hε
+    hf_mk.integral_indicator_norm_ge_nonneg_le_of_meas hf.1.stronglyMeasurable_mk hε
   refine' ⟨M, hM_pos, (le_of_eq _).trans hfM⟩
   refine' lintegral_congr_ae _
   filter_upwards [hf.1.ae_eq_mk] with x hx
@@ -263,7 +263,7 @@ theorem Memℒp.snorm_indicator_norm_ge_le (hf : Memℒp f p μ) (hmeas : Strong
     simp [snorm_exponent_zero]
   by_cases hp_ne_top : p = ∞
   · subst hp_ne_top
-    obtain ⟨M, hM⟩ := hf.snormEssSup_indicator_norm_ge_eq_zero μ hmeas
+    obtain ⟨M, hM⟩ := hf.snormEssSup_indicator_norm_ge_eq_zero hmeas
     refine' ⟨M, _⟩
     simp only [snorm_exponent_top, hM, zero_le]
   obtain ⟨M, hM', hM⟩ := Memℒp.integral_indicator_norm_ge_nonneg_le
@@ -297,7 +297,7 @@ theorem Memℒp.snorm_indicator_norm_ge_le (hf : Memℒp f p μ) (hmeas : Strong
 theorem Memℒp.snorm_indicator_norm_ge_pos_le (hf : Memℒp f p μ) (hmeas : StronglyMeasurable f)
     {ε : ℝ} (hε : 0 < ε) :
     ∃ M : ℝ, 0 < M ∧ snorm ({ x | M ≤ ‖f x‖₊ }.indicator f) p μ ≤ ENNReal.ofReal ε := by
-  obtain ⟨M, hM⟩ := hf.snorm_indicator_norm_ge_le μ hmeas hε
+  obtain ⟨M, hM⟩ := hf.snorm_indicator_norm_ge_le hmeas hε
   refine'
     ⟨max M 1, lt_of_lt_of_le zero_lt_one (le_max_right _ _), le_trans (snorm_mono fun x => _) hM⟩
   rw [norm_indicator_eq_indicator_norm, norm_indicator_eq_indicator_norm]
@@ -346,9 +346,9 @@ theorem Memℒp.snorm_indicator_le' (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) (hf
     (hmeas : StronglyMeasurable f) {ε : ℝ} (hε : 0 < ε) :
     ∃ (δ : ℝ) (hδ : 0 < δ), ∀ s, MeasurableSet s → μ s ≤ ENNReal.ofReal δ →
       snorm (s.indicator f) p μ ≤ 2 * ENNReal.ofReal ε := by
-  obtain ⟨M, hMpos, hM⟩ := hf.snorm_indicator_norm_ge_pos_le μ hmeas hε
+  obtain ⟨M, hMpos, hM⟩ := hf.snorm_indicator_norm_ge_pos_le hmeas hε
   obtain ⟨δ, hδpos, hδ⟩ :=
-    snorm_indicator_le_of_bound μ (f := { x | ‖f x‖ < M }.indicator f) hp_top hε (by
+    snorm_indicator_le_of_bound (f := { x | ‖f x‖ < M }.indicator f) hp_top hε (by
       intro x
       rw [norm_indicator_eq_indicator_norm, Set.indicator_apply]
       split_ifs with h
@@ -378,7 +378,7 @@ theorem Memℒp.snorm_indicator_le_of_meas (hp_one : 1 ≤ p) (hp_top : p ≠ 
     (hmeas : StronglyMeasurable f) {ε : ℝ} (hε : 0 < ε) :
     ∃ (δ : ℝ) (hδ : 0 < δ), ∀ s, MeasurableSet s → μ s ≤ ENNReal.ofReal δ →
       snorm (s.indicator f) p μ ≤ ENNReal.ofReal ε := by
-  obtain ⟨δ, hδpos, hδ⟩ := hf.snorm_indicator_le' μ hp_one hp_top hmeas (half_pos hε)
+  obtain ⟨δ, hδpos, hδ⟩ := hf.snorm_indicator_le' hp_one hp_top hmeas (half_pos hε)
   refine' ⟨δ, hδpos, fun s hs hμs => le_trans (hδ s hs hμs) _⟩
   rw [ENNReal.ofReal_div_of_pos zero_lt_two, (by norm_num : ENNReal.ofReal 2 = 2),
       ENNReal.mul_div_cancel'] <;>
@@ -391,7 +391,7 @@ theorem Memℒp.snorm_indicator_le (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) (hf :
       snorm (s.indicator f) p μ ≤ ENNReal.ofReal ε := by
   have hℒp := hf
   obtain ⟨⟨f', hf', heq⟩, _⟩ := hf
-  obtain ⟨δ, hδpos, hδ⟩ := (hℒp.ae_eq heq).snorm_indicator_le_of_meas μ hp_one hp_top hf' hε
+  obtain ⟨δ, hδpos, hδ⟩ := (hℒp.ae_eq heq).snorm_indicator_le_of_meas hp_one hp_top hf' hε
   refine' ⟨δ, hδpos, fun s hs hμs => _⟩
   convert hδ s hs hμs using 1
   rw [snorm_indicator_eq_snorm_restrict hs, snorm_indicator_eq_snorm_restrict hs]
@@ -402,7 +402,7 @@ theorem Memℒp.snorm_indicator_le (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) (hf :
 theorem unifIntegrable_const {g : α → β} (hp : 1 ≤ p) (hp_ne_top : p ≠ ∞) (hg : Memℒp g p μ) :
     UnifIntegrable (fun _ : ι => g) p μ := by
   intro ε hε
-  obtain ⟨δ, hδ_pos, hgδ⟩ := hg.snorm_indicator_le μ hp hp_ne_top hε
+  obtain ⟨δ, hδ_pos, hgδ⟩ := hg.snorm_indicator_le hp hp_ne_top hε
   exact ⟨δ, hδ_pos, fun _ => hgδ⟩
 #align measure_theory.unif_integrable_const MeasureTheory.unifIntegrable_const
 
@@ -412,7 +412,7 @@ theorem unifIntegrable_subsingleton [Subsingleton ι] (hp_one : 1 ≤ p) (hp_top
   intro ε hε
   by_cases hι : Nonempty ι
   · cases' hι with i
-    obtain ⟨δ, hδpos, hδ⟩ := (hf i).snorm_indicator_le μ hp_one hp_top hε
+    obtain ⟨δ, hδpos, hδ⟩ := (hf i).snorm_indicator_le hp_one hp_top hε
     refine' ⟨δ, hδpos, fun j s hs hμs => _⟩
     convert hδ s hs hμs
   · exact ⟨1, zero_lt_one, fun i => False.elim <| hι <| Nonempty.intro i⟩
@@ -426,12 +426,12 @@ theorem unifIntegrable_fin (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) {n : ℕ} {f
   induction' n with n h
   · intro f hf
     have : Subsingleton (Fin Nat.zero) := subsingleton_fin_zero -- Porting note: Added this instance
-    exact unifIntegrable_subsingleton μ hp_one hp_top hf
+    exact unifIntegrable_subsingleton hp_one hp_top hf
   intro f hfLp ε hε
   let g : Fin n → α → β := fun k => f k
   have hgLp : ∀ i, Memℒp (g i) p μ := fun i => hfLp i
   obtain ⟨δ₁, hδ₁pos, hδ₁⟩ := h hgLp hε
-  obtain ⟨δ₂, hδ₂pos, hδ₂⟩ := (hfLp n).snorm_indicator_le μ hp_one hp_top hε
+  obtain ⟨δ₂, hδ₂pos, hδ₂⟩ := (hfLp n).snorm_indicator_le hp_one hp_top hε
   refine' ⟨min δ₁ δ₂, lt_min hδ₁pos hδ₂pos, fun i s hs hμs => _⟩
   by_cases hi : i.val < n
   · rw [(_ : f i = g ⟨i.val, hi⟩)]
@@ -453,7 +453,7 @@ theorem unifIntegrable_finite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞
   intro ε hε
   let g : Fin n → α → β := f ∘ hn.some.symm
   have hg : ∀ i, Memℒp (g i) p μ := fun _ => hf _
-  obtain ⟨δ, hδpos, hδ⟩ := unifIntegrable_fin μ hp_one hp_top hg hε
+  obtain ⟨δ, hδpos, hδ⟩ := unifIntegrable_fin hp_one hp_top hg hε
   refine' ⟨δ, hδpos, fun i s hs hμs => _⟩
   specialize hδ (hn.some i) s hs hμs
   simp_rw [Function.comp_apply, Equiv.symm_apply_apply] at hδ
@@ -462,7 +462,8 @@ theorem unifIntegrable_finite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞
 
 end
 
-theorem snorm_sub_le_of_dist_bdd {p : ℝ≥0∞} (hp' : p ≠ ∞) {s : Set α} (hs : MeasurableSet[m] s)
+theorem snorm_sub_le_of_dist_bdd (μ : Measure α)
+    {p : ℝ≥0∞} (hp' : p ≠ ∞) {s : Set α} (hs : MeasurableSet[m] s)
     {f g : α → β} {c : ℝ} (hc : 0 ≤ c) (hf : ∀ x ∈ s, dist (f x) (g x) ≤ c) :
     snorm (s.indicator (f - g)) p μ ≤ ENNReal.ofReal c * μ s ^ (1 / p.toReal) := by
   by_cases hp : p = 0
@@ -502,7 +503,7 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp
   have hpow : 0 < measureUnivNNReal μ ^ (1 / p.toReal) :=
     Real.rpow_pos_of_pos (measureUnivNNReal_pos hμ) _
   obtain ⟨δ₁, hδ₁, hsnorm₁⟩ := hui hε'
-  obtain ⟨δ₂, hδ₂, hsnorm₂⟩ := hg'.snorm_indicator_le μ hp hp' hε'
+  obtain ⟨δ₂, hδ₂, hsnorm₂⟩ := hg'.snorm_indicator_le hp hp' hε'
   obtain ⟨t, htm, ht₁, ht₂⟩ := tendstoUniformlyOn_of_ae_tendsto' hf hg hfg (lt_min hδ₁ hδ₂)
   rw [Metric.tendstoUniformlyOn_iff] at ht₂
   specialize ht₂ (ε.toReal / (3 * measureUnivNNReal μ ^ (1 / p.toReal)))
@@ -557,7 +558,7 @@ theorem tendsto_Lp_of_tendsto_ae [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p 
   have : ∀ n, snorm (f n - g) p μ = snorm ((hf n).mk (f n) - hg.1.mk g) p μ :=
     fun n => snorm_congr_ae ((hf n).ae_eq_mk.sub hg.1.ae_eq_mk)
   simp_rw [this]
-  refine' tendsto_Lp_of_tendsto_ae_of_meas μ hp hp' (fun n => (hf n).stronglyMeasurable_mk)
+  refine' tendsto_Lp_of_tendsto_ae_of_meas hp hp' (fun n => (hf n).stronglyMeasurable_mk)
     hg.1.stronglyMeasurable_mk (hg.ae_eq hg.1.ae_eq_mk) (hui.ae_eq fun n => (hf n).ae_eq_mk) _
   have h_ae_forall_eq : ∀ᵐ x ∂μ, ∀ n, f n x = (hf n).mk (f n) x := by
     rw [ae_all_iff]
@@ -579,7 +580,7 @@ theorem unifIntegrable_of_tendsto_Lp_zero (hp : 1 ≤ p) (hp' : p ≠ ∞) (hf :
   obtain ⟨N, hN⟩ := hf_tendsto (ENNReal.ofReal ε) (by simpa)
   let F : Fin N → α → β := fun n => f n
   have hF : ∀ n, Memℒp (F n) p μ := fun n => hf n
-  obtain ⟨δ₁, hδpos₁, hδ₁⟩ := unifIntegrable_fin μ hp hp' hF hε
+  obtain ⟨δ₁, hδpos₁, hδ₁⟩ := unifIntegrable_fin hp hp' hF hε
   refine' ⟨δ₁, hδpos₁, fun n s hs hμs => _⟩
   by_cases hn : n < N
   · exact hδ₁ ⟨n, hn⟩ s hs hμs
@@ -595,8 +596,8 @@ theorem unifIntegrable_of_tendsto_Lp (hp : 1 ≤ p) (hp' : p ≠ ∞) (hf : ∀
   rw [this]
   refine' UnifIntegrable.add _ _ hp (fun _ => hg.aestronglyMeasurable)
       fun n => (hf n).1.sub hg.aestronglyMeasurable
-  · exact unifIntegrable_const μ hp hp' hg
-  · exact unifIntegrable_of_tendsto_Lp_zero μ hp hp' (fun n => (hf n).sub hg) hfg
+  · exact unifIntegrable_const hp hp' hg
+  · exact unifIntegrable_of_tendsto_Lp_zero hp hp' (fun n => (hf n).sub hg) hfg
 set_option linter.uppercaseLean3 false in
 #align measure_theory.unif_integrable_of_tendsto_Lp MeasureTheory.unifIntegrable_of_tendsto_Lp
 
@@ -609,7 +610,7 @@ theorem tendsto_Lp_of_tendstoInMeasure [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp'
   refine' tendsto_of_subseq_tendsto fun ns hns => _
   obtain ⟨ms, _, hms'⟩ := TendstoInMeasure.exists_seq_tendsto_ae fun ε hε => (hfg ε hε).comp hns
   exact ⟨ms,
-    tendsto_Lp_of_tendsto_ae μ hp hp' (fun _ => hf _) hg (fun ε hε =>
+    tendsto_Lp_of_tendsto_ae hp hp' (fun _ => hf _) hg (fun ε hε =>
       let ⟨δ, hδ, hδ'⟩ := hui hε
       ⟨δ, hδ, fun i s hs hμs => hδ' _ s hs hμs⟩)
       hms'⟩
@@ -622,10 +623,10 @@ theorem tendstoInMeasure_iff_tendsto_Lp [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp'
     (hf : ∀ n, Memℒp (f n) p μ) (hg : Memℒp g p μ) :
     TendstoInMeasure μ f atTop g ∧ UnifIntegrable f p μ ↔
       Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0) :=
-  ⟨fun h => tendsto_Lp_of_tendstoInMeasure μ hp hp' (fun n => (hf n).1) hg h.2 h.1, fun h =>
+  ⟨fun h => tendsto_Lp_of_tendstoInMeasure hp hp' (fun n => (hf n).1) hg h.2 h.1, fun h =>
     ⟨tendstoInMeasure_of_tendsto_snorm (lt_of_lt_of_le zero_lt_one hp).ne.symm
         (fun n => (hf n).aestronglyMeasurable) hg.aestronglyMeasurable h,
-      unifIntegrable_of_tendsto_Lp μ hp hp' hf hg h⟩⟩
+      unifIntegrable_of_tendsto_Lp hp hp' hf hg h⟩⟩
 set_option linter.uppercaseLean3 false in
 #align measure_theory.tendsto_in_measure_iff_tendsto_Lp MeasureTheory.tendstoInMeasure_iff_tendsto_Lp
 
@@ -702,7 +703,7 @@ theorem unifIntegrable_of (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ι → α → β
     UnifIntegrable f p μ := by
   set g : ι → α → β := fun i => (hf i).choose
   refine'
-    (unifIntegrable_of' μ hp hp' (fun i => (Exists.choose_spec <| hf i).1) fun ε hε => _).ae_eq
+    (unifIntegrable_of' hp hp' (fun i => (Exists.choose_spec <| hf i).1) fun ε hε => _).ae_eq
       fun i => (Exists.choose_spec <| hf i).2.symm
   obtain ⟨C, hC⟩ := h ε hε
   have hCg : ∀ i, snorm ({ x | C ≤ ‖g i x‖₊ }.indicator (g i)) p μ ≤ ENNReal.ofReal ε := by
@@ -759,7 +760,7 @@ theorem uniformIntegrable_congr_ae {g : ι → α → β} (hfg : ∀ n, f n =ᵐ
 theorem uniformIntegrable_finite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞)
     (hf : ∀ i, Memℒp (f i) p μ) : UniformIntegrable f p μ := by
   cases nonempty_fintype ι
-  refine' ⟨fun n => (hf n).1, unifIntegrable_finite μ hp_one hp_top hf, _⟩
+  refine' ⟨fun n => (hf n).1, unifIntegrable_finite hp_one hp_top hf, _⟩
   by_cases hι : Nonempty ι
   · choose _ hf using hf
     set C := (Finset.univ.image fun i : ι => snorm (f i) p μ).max'
@@ -783,7 +784,7 @@ theorem uniformIntegrable_subsingleton [Subsingleton ι] (hp_one : 1 ≤ p) (hp_
 /-- A constant sequence of functions is uniformly integrable in the probability sense. -/
 theorem uniformIntegrable_const {g : α → β} (hp : 1 ≤ p) (hp_ne_top : p ≠ ∞) (hg : Memℒp g p μ) :
     UniformIntegrable (fun _ : ι => g) p μ :=
-  ⟨fun _ => hg.1, unifIntegrable_const μ hp hp_ne_top hg,
+  ⟨fun _ => hg.1, unifIntegrable_const hp hp_ne_top hg,
     ⟨(snorm g p μ).toNNReal, fun _ => le_of_eq (ENNReal.coe_toNNReal hg.2.ne).symm⟩⟩
 #align measure_theory.uniform_integrable_const MeasureTheory.uniformIntegrable_const
 
@@ -795,7 +796,7 @@ theorem uniformIntegrable_of' [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ 
       ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε) :
     UniformIntegrable f p μ := by
   refine' ⟨fun i => (hf i).aestronglyMeasurable,
-    unifIntegrable_of μ hp hp' (fun i => (hf i).aestronglyMeasurable) h, _⟩
+    unifIntegrable_of hp hp' (fun i => (hf i).aestronglyMeasurable) h, _⟩
   obtain ⟨C, hC⟩ := h 1 one_pos
   refine' ⟨((C : ℝ≥0∞) * μ Set.univ ^ p.toReal⁻¹ + 1).toNNReal, fun i => _⟩
   calc

by tweaking the definition of the AddMonoid and MonoidWithZero instances for WithTop. Also unprotect ENNReal.coe_injective and rename ENNReal.coe_eq_coe → ENNReal.coe_inj.

From LeanAPAP

@@ -225,7 +225,7 @@ theorem Memℒp.integral_indicator_norm_ge_nonneg_le (hf : Memℒp f 1 μ) {ε :
   refine' ⟨M, hM_pos, (le_of_eq _).trans hfM⟩
   refine' lintegral_congr_ae _
   filter_upwards [hf.1.ae_eq_mk] with x hx
-  simp only [Set.indicator_apply, coe_nnnorm, Set.mem_setOf_eq, ENNReal.coe_eq_coe, hx.symm]
+  simp only [Set.indicator_apply, coe_nnnorm, Set.mem_setOf_eq, ENNReal.coe_inj, hx.symm]
 #align measure_theory.mem_ℒp.integral_indicator_norm_ge_nonneg_le MeasureTheory.Memℒp.integral_indicator_norm_ge_nonneg_le
 
 theorem Memℒp.snormEssSup_indicator_norm_ge_eq_zero (hf : Memℒp f ∞ μ)

@@ -525,9 +525,7 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp
     exact min_le_right _ _
   have hlt : snorm (tᶜ.indicator (f n - g)) p μ ≤ ENNReal.ofReal (ε.toReal / 3) := by
     specialize hN n hn
-    have : 0 ≤ ε.toReal / (3 * measureUnivNNReal μ ^ (1 / p.toReal)) := by
-      rw [div_mul_eq_div_mul_one_div]
-      exact mul_nonneg hε'.le (one_div_nonneg.2 hpow.le)
+    have : 0 ≤ ε.toReal / (3 * measureUnivNNReal μ ^ (1 / p.toReal)) := by positivity
     have := snorm_sub_le_of_dist_bdd μ hp' htm.compl this fun x hx =>
       (dist_comm (g x) (f n x) ▸ (hN x hx).le :
         dist (f n x) (g x) ≤ ε.toReal / (3 * measureUnivNNReal μ ^ (1 / p.toReal)))
@@ -541,7 +539,7 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp
         rw [ENNReal.ofReal_coe_nnreal, coe_measureUnivNNReal]
         exact measure_mono (Set.subset_univ _)
       · exact Real.rpow_pos_of_pos (measureUnivNNReal_pos hμ) _
-    · refine' mul_nonneg hε'.le (one_div_nonneg.2 hpow.le)
+    · positivity
   have : ENNReal.ofReal (ε.toReal / 3) = ε / 3 := by
     rw [ENNReal.ofReal_div_of_pos (show (0 : ℝ) < 3 by norm_num), ENNReal.ofReal_toReal h.ne]
     simp

This better matches other lemma names.

From LeanAPAP

@@ -280,7 +280,7 @@ theorem Memℒp.snorm_indicator_norm_ge_le (hf : Memℒp f p μ) (hmeas : Strong
     nnnorm_indicator_eq_indicator_nnnorm]
   have hiff : M ^ (1 / p.toReal) ≤ ‖f x‖₊ ↔ M ≤ ‖‖f x‖ ^ p.toReal‖₊ := by
     rw [coe_nnnorm, coe_nnnorm, Real.norm_rpow_of_nonneg (norm_nonneg _), norm_norm,
-      ← Real.rpow_le_rpow_iff hM' (Real.rpow_nonneg_of_nonneg (norm_nonneg _) _)
+      ← Real.rpow_le_rpow_iff hM' (Real.rpow_nonneg (norm_nonneg _) _)
         (one_div_pos.2 <| ENNReal.toReal_pos hp_ne_zero hp_ne_top), ← Real.rpow_mul (norm_nonneg _),
       mul_one_div_cancel (ENNReal.toReal_pos hp_ne_zero hp_ne_top).ne.symm, Real.rpow_one]
   by_cases hx : x ∈ { x : α | M ^ (1 / p.toReal) ≤ ‖f x‖₊ }

Function.support is a very basic definition. Nevertheless, it is a pretty heavy import because it imports most objects a support lemma can be written about.

This PR reverses the dependencies between those objects and Function.support, so that the latter can become a much more lightweight import.

Only two import could not easily be reversed, namely the ones to Data.Set.Finite and Order.ConditionallyCompleteLattice.Basic, so I created two new files instead.

I credit:

• Yury for https://github.com/leanprover-community/mathlib/pull/6791
• Oliver for https://github.com/leanprover-community/mathlib/pull/7439

@@ -926,7 +926,7 @@ theorem uniformIntegrable_average
   · exact (Finset.aestronglyMeasurable_sum' _ fun i _ => hf₁ i).const_smul _
   · obtain ⟨δ, hδ₁, hδ₂⟩ := hf₂ hε
     refine' ⟨δ, hδ₁, fun n s hs hle => _⟩
-    simp_rw [Finset.smul_sum, Set.indicator_finset_sum]
+    simp_rw [Finset.smul_sum, Finset.indicator_sum]
     refine' le_trans (snorm_sum_le (fun i _ => ((hf₁ i).const_smul _).indicator hs) hp) _
     have : ∀ i, s.indicator ((n : ℝ) ⁻¹ • f i) = (↑n : ℝ)⁻¹ • s.indicator (f i) :=
       fun i ↦ indicator_const_smul _ _ _

I've also got a change to make this required, but I'd like to land this first.

@@ -488,7 +488,7 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp
     Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0) := by
   rw [ENNReal.tendsto_atTop_zero]
   intro ε hε
-  by_cases ε < ∞; swap
+  by_cases h : ε < ∞; swap
   · rw [not_lt, top_le_iff] at h
     exact ⟨0, fun n _ => by simp [h]⟩
   by_cases hμ : μ = 0

@@ -876,13 +876,13 @@ theorem UniformIntegrable.spec' (hp : p ≠ 0) (hp' : p ≠ ∞) (hf : ∀ i, St
             (eventually_of_forall fun x hx => _)
           rwa [nnnorm_indicator_eq_indicator_nnnorm, Set.indicator_of_mem hx]
         _ ≤ snorm (f (ℐ C)) p μ := snorm_indicator_le _
-    specialize this (2 * max M 1 * HPow.hPow δ⁻¹ (1 / p.toReal))
+    specialize this (2 * max M 1 * δ⁻¹ ^ (1 / p.toReal))
     rw [ENNReal.coe_rpow_of_nonneg _ (one_div_nonneg.2 ENNReal.toReal_nonneg), ← ENNReal.coe_smul,
       smul_eq_mul, mul_assoc, NNReal.inv_rpow,
       inv_mul_cancel (NNReal.rpow_pos (NNReal.coe_pos.1 hδpos)).ne.symm, mul_one, ENNReal.coe_mul,
       ← NNReal.inv_rpow] at this
     refine' (lt_of_le_of_lt (le_trans
-      (hM <| ℐ <| 2 * max M 1 * HPow.hPow δ⁻¹ (1 / p.toReal)) (le_max_left (M : ℝ≥0∞) 1))
+      (hM <| ℐ <| 2 * max M 1 * δ⁻¹ ^ (1 / p.toReal)) (le_max_left (M : ℝ≥0∞) 1))
         (lt_of_lt_of_le _ this)).ne rfl
     rw [← ENNReal.coe_one, ← ENNReal.coe_max, ← ENNReal.coe_mul, ENNReal.coe_lt_coe]
     exact lt_two_mul_self (lt_max_of_lt_right one_pos)

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -950,11 +950,9 @@ theorem uniformIntegrable_average
     refine' le_trans _ (_ : ↑(↑n : ℝ≥0)⁻¹ * (n • C : ℝ≥0∞) ≤ C)
     · refine' (ENNReal.mul_le_mul_left hn ENNReal.coe_ne_top).2 _
       conv_rhs => rw [← Finset.card_range n]
-      -- Porting note: Originally `exact Finset.sum_le_card_nsmul _ _ _ fun i hi => hC i`
-      convert Finset.sum_le_card_nsmul _ _ _ fun i _ => hC i
-      rw [ENNReal.coe_smul]
+      exact Finset.sum_le_card_nsmul _ _ _ fun i _ => hC i
     · simp only [ENNReal.coe_eq_zero, inv_eq_zero, Nat.cast_eq_zero] at hn
-      rw [ENNReal.coe_smul, nsmul_eq_mul, ← mul_assoc, ENNReal.coe_inv, ENNReal.coe_nat,
+      rw [nsmul_eq_mul, ← mul_assoc, ENNReal.coe_inv, ENNReal.coe_nat,
         ENNReal.inv_mul_cancel _ (ENNReal.nat_ne_top _), one_mul]
       all_goals simpa only [Ne.def, Nat.cast_eq_zero]
 

This eliminates (fun a ↦ β) α in the type when applying a FunLike.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -451,12 +451,12 @@ theorem unifIntegrable_finite [Finite ι] (hp_one : 1 ≤ p) (hp_top : p ≠ ∞
     (hf : ∀ i, Memℒp (f i) p μ) : UnifIntegrable f p μ := by
   obtain ⟨n, hn⟩ := Finite.exists_equiv_fin ι
   intro ε hε
-  set g : Fin n → α → β := f ∘ hn.some.symm with hgeq
+  let g : Fin n → α → β := f ∘ hn.some.symm
   have hg : ∀ i, Memℒp (g i) p μ := fun _ => hf _
   obtain ⟨δ, hδpos, hδ⟩ := unifIntegrable_fin μ hp_one hp_top hg hε
   refine' ⟨δ, hδpos, fun i s hs hμs => _⟩
   specialize hδ (hn.some i) s hs hμs
-  simp_rw [hgeq, Function.comp_apply, Equiv.symm_apply_apply] at hδ
+  simp_rw [Function.comp_apply, Equiv.symm_apply_apply] at hδ
   assumption
 #align measure_theory.unif_integrable_finite MeasureTheory.unifIntegrable_finite
 

We already have the strong law of large numbers for real-valued integrable random variables. We generalize it to general vector-valued integrable random variables. This does not require any second-countability assumptions as integrable functions can by definition be approximated by simple functions, for which the result is deduced from the one-dimensional one.

Along the way, we extend a few lemmas in the library from the real case to the vector case, and remove unneeded second-countability assumptions.

@@ -917,23 +917,19 @@ theorem uniformIntegrable_iff [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ 
 #align measure_theory.uniform_integrable_iff MeasureTheory.uniformIntegrable_iff
 
 /-- The averaging of a uniformly integrable sequence is also uniformly integrable. -/
-theorem uniformIntegrable_average (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf : UniformIntegrable f p μ) :
-    UniformIntegrable (fun n => (∑ i in Finset.range n, f i) / (n : α → ℝ)) p μ := by
+theorem uniformIntegrable_average
+    {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
+    (hp : 1 ≤ p) {f : ℕ → α → E} (hf : UniformIntegrable f p μ) :
+    UniformIntegrable (fun (n : ℕ) => (n : ℝ)⁻¹ • (∑ i in Finset.range n, f i)) p μ := by
   obtain ⟨hf₁, hf₂, hf₃⟩ := hf
   refine' ⟨fun n => _, fun ε hε => _, _⟩
-  · simp_rw [div_eq_mul_inv]
-    exact (Finset.aestronglyMeasurable_sum' _ fun i _ => hf₁ i).mul
-      (aestronglyMeasurable_const : AEStronglyMeasurable (fun _ => (↑n : ℝ)⁻¹) μ)
+  · exact (Finset.aestronglyMeasurable_sum' _ fun i _ => hf₁ i).const_smul _
   · obtain ⟨δ, hδ₁, hδ₂⟩ := hf₂ hε
     refine' ⟨δ, hδ₁, fun n s hs hle => _⟩
-    simp_rw [div_eq_mul_inv, Finset.sum_mul, Set.indicator_finset_sum]
-    refine' le_trans (snorm_sum_le (fun i _ => ((hf₁ i).mul_const (↑n)⁻¹).indicator hs) hp) _
-    have : ∀ i, s.indicator (f i * (n : α → ℝ)⁻¹) = (↑n : ℝ)⁻¹ • s.indicator (f i) := by
-      intro i
-      rw [mul_comm, (_ : (↑n)⁻¹ * f i = fun ω => (↑n : ℝ)⁻¹ • f i ω)]
-      · rw [Set.indicator_const_smul s (↑n : ℝ)⁻¹ (f i)]
-        rfl
-      · rfl
+    simp_rw [Finset.smul_sum, Set.indicator_finset_sum]
+    refine' le_trans (snorm_sum_le (fun i _ => ((hf₁ i).const_smul _).indicator hs) hp) _
+    have : ∀ i, s.indicator ((n : ℝ) ⁻¹ • f i) = (↑n : ℝ)⁻¹ • s.indicator (f i) :=
+      fun i ↦ indicator_const_smul _ _ _
     simp_rw [this, snorm_const_smul, ← Finset.mul_sum, nnnorm_inv, Real.nnnorm_coe_nat]
     by_cases hn : (↑(↑n : ℝ≥0)⁻¹ : ℝ≥0∞) = 0
     · simp only [hn, zero_mul, zero_le]
@@ -946,13 +942,9 @@ theorem uniformIntegrable_average (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf :
         ENNReal.inv_mul_cancel _ (ENNReal.nat_ne_top _), one_mul]
       all_goals simpa only [Ne.def, Nat.cast_eq_zero]
   · obtain ⟨C, hC⟩ := hf₃
-    simp_rw [div_eq_mul_inv, Finset.sum_mul]
-    refine' ⟨C, fun n => (snorm_sum_le (fun i _ => (hf₁ i).mul_const (↑n)⁻¹) hp).trans _⟩
-    have : ∀ i, (fun ω => f i ω * (↑n)⁻¹) = (↑n : ℝ)⁻¹ • fun ω => f i ω := by
-      intro i
-      ext ω
-      simp only [mul_comm, Pi.smul_apply, Algebra.id.smul_eq_mul]
-    simp_rw [this, snorm_const_smul, ← Finset.mul_sum, nnnorm_inv, Real.nnnorm_coe_nat]
+    simp_rw [Finset.smul_sum]
+    refine' ⟨C, fun n => (snorm_sum_le (fun i _ => (hf₁ i).const_smul _) hp).trans _⟩
+    simp_rw [snorm_const_smul, ← Finset.mul_sum, nnnorm_inv, Real.nnnorm_coe_nat]
     by_cases hn : (↑(↑n : ℝ≥0)⁻¹ : ℝ≥0∞) = 0
     · simp only [hn, zero_mul, zero_le]
     refine' le_trans _ (_ : ↑(↑n : ℝ≥0)⁻¹ * (n • C : ℝ≥0∞) ≤ C)
@@ -965,7 +957,14 @@ theorem uniformIntegrable_average (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf :
       rw [ENNReal.coe_smul, nsmul_eq_mul, ← mul_assoc, ENNReal.coe_inv, ENNReal.coe_nat,
         ENNReal.inv_mul_cancel _ (ENNReal.nat_ne_top _), one_mul]
       all_goals simpa only [Ne.def, Nat.cast_eq_zero]
-#align measure_theory.uniform_integrable_average MeasureTheory.uniformIntegrable_average
+
+/-- The averaging of a uniformly integrable real-valued sequence is also uniformly integrable. -/
+theorem uniformIntegrable_average_real (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf : UniformIntegrable f p μ) :
+    UniformIntegrable (fun n => (∑ i in Finset.range n, f i) / (n : α → ℝ)) p μ := by
+  convert uniformIntegrable_average hp hf using 2 with n
+  ext x
+  simp [div_eq_inv_mul]
+#align measure_theory.uniform_integrable_average MeasureTheory.uniformIntegrable_average_real
 
 end UniformIntegrable
 

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -936,7 +936,7 @@ theorem uniformIntegrable_average (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf :
       · rfl
     simp_rw [this, snorm_const_smul, ← Finset.mul_sum, nnnorm_inv, Real.nnnorm_coe_nat]
     by_cases hn : (↑(↑n : ℝ≥0)⁻¹ : ℝ≥0∞) = 0
-    · simp only [hn, MulZeroClass.zero_mul, zero_le]
+    · simp only [hn, zero_mul, zero_le]
     refine' le_trans _ (_ : ↑(↑n : ℝ≥0)⁻¹ * n • ENNReal.ofReal ε ≤ ENNReal.ofReal ε)
     · refine' (ENNReal.mul_le_mul_left hn ENNReal.coe_ne_top).2 _
       conv_rhs => rw [← Finset.card_range n]
@@ -954,7 +954,7 @@ theorem uniformIntegrable_average (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf :
       simp only [mul_comm, Pi.smul_apply, Algebra.id.smul_eq_mul]
     simp_rw [this, snorm_const_smul, ← Finset.mul_sum, nnnorm_inv, Real.nnnorm_coe_nat]
     by_cases hn : (↑(↑n : ℝ≥0)⁻¹ : ℝ≥0∞) = 0
-    · simp only [hn, MulZeroClass.zero_mul, zero_le]
+    · simp only [hn, zero_mul, zero_le]
     refine' le_trans _ (_ : ↑(↑n : ℝ≥0)⁻¹ * (n • C : ℝ≥0∞) ≤ C)
     · refine' (ENNReal.mul_le_mul_left hn ENNReal.coe_ne_top).2 _
       conv_rhs => rw [← Finset.card_range n]

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -53,7 +53,7 @@ namespace MeasureTheory
 
 open Set Filter TopologicalSpace
 
-variable {α β ι : Type _} {m : MeasurableSpace α} {μ : Measure α} [NormedAddCommGroup β]
+variable {α β ι : Type*} {m : MeasurableSpace α} {μ : Measure α} [NormedAddCommGroup β]
 
 /-- Uniform integrability in the measure theory sense.
 

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
-
-! This file was ported from Lean 3 source module measure_theory.function.uniform_integrable
-! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Function.ConvergenceInMeasure
 import Mathlib.MeasureTheory.Function.L1Space
 
+#align_import measure_theory.function.uniform_integrable from "leanprover-community/mathlib"@"57ac39bd365c2f80589a700f9fbb664d3a1a30c2"
+
 /-!
 # Uniform integrability
 

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -535,7 +535,7 @@ theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp
       (dist_comm (g x) (f n x) ▸ (hN x hx).le :
         dist (f n x) (g x) ≤ ε.toReal / (3 * measureUnivNNReal μ ^ (1 / p.toReal)))
     refine' le_trans this _
-    rw [div_mul_eq_div_mul_one_div, ← ENNReal.ofReal_toReal (measure_lt_top μ (tᶜ)).ne,
+    rw [div_mul_eq_div_mul_one_div, ← ENNReal.ofReal_toReal (measure_lt_top μ tᶜ).ne,
       ENNReal.ofReal_rpow_of_nonneg ENNReal.toReal_nonneg hdivp, ← ENNReal.ofReal_mul, mul_assoc]
     · refine' ENNReal.ofReal_le_ofReal (mul_le_of_le_one_right hε'.le _)
       rw [mul_comm, mul_one_div, div_le_one]

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -862,7 +862,7 @@ theorem UniformIntegrable.spec' (hp : p ≠ 0) (hp' : p ≠ ∞) (hf : ∀ i, St
   obtain ⟨-, hfu, M, hM⟩ := hfu
   obtain ⟨δ, hδpos, hδ⟩ := hfu hε
   obtain ⟨C, hC⟩ : ∃ C : ℝ≥0, ∀ i, μ { x | C ≤ ‖f i x‖₊ } ≤ ENNReal.ofReal δ := by
-    by_contra hcon; push_neg  at hcon
+    by_contra hcon; push_neg at hcon
     choose ℐ hℐ using hcon
     lift δ to ℝ≥0 using hδpos.le
     have : ∀ C : ℝ≥0, C • (δ : ℝ≥0∞) ^ (1 / p.toReal) ≤ snorm (f (ℐ C)) p μ := by

These are all doc fixes

@@ -16,11 +16,11 @@ import Mathlib.MeasureTheory.Function.L1Space
 
 This file contains the definitions for uniform integrability (both in the measure theory sense
 as well as the probability theory sense). This file also contains the Vitali convergence theorem
-which estabishes a relation between uniform integrability, convergence in measure and
+which establishes a relation between uniform integrability, convergence in measure and
 Lp convergence.
 
 Uniform integrability plays a vital role in the theory of martingales most notably is used to
-fomulate the martingale convergence theorem.
+formulate the martingale convergence theorem.
 
 ## Main definitions
 
@@ -64,7 +64,7 @@ A sequence of functions `f` is said to be uniformly integrable if for all `ε >
 some `δ > 0` such that for all sets `s` with measure less than `δ`, the Lp-norm of `f i`
 restricted on `s` is less than `ε`.
 
-Uniform integrablility is also known as uniformly absolutely continuous integrals. -/
+Uniform integrability is also known as uniformly absolutely continuous integrals. -/
 def UnifIntegrable {_ : MeasurableSpace α} (f : ι → α → β) (p : ℝ≥0∞) (μ : Measure α) : Prop :=
   ∀ ⦃ε : ℝ⦄ (_ : 0 < ε), ∃ (δ : ℝ) (_ : 0 < δ), ∀ i s,
     MeasurableSet s → μ s ≤ ENNReal.ofReal δ → snorm (s.indicator (f i)) p μ ≤ ENNReal.ofReal ε
@@ -834,7 +834,7 @@ theorem uniformIntegrable_of' [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ 
         ENNReal.one_ne_top⟩
 #align measure_theory.uniform_integrable_of' MeasureTheory.uniformIntegrable_of'
 
-/-- A sequene of functions `(fₙ)` is uniformly integrable in the probability sense if for all
+/-- A sequence of functions `(fₙ)` is uniformly integrable in the probability sense if for all
 `ε > 0`, there exists some `C` such that `∫ x in {|fₙ| ≥ C}, fₙ x ∂μ ≤ ε` for all `n`. -/
 theorem uniformIntegrable_of [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
     (hf : ∀ i, AEStronglyMeasurable (f i) μ)

I have misported is_foo to Foo because I misunderstood the rule for IsLawfulFoo. This PR recover Is of Foo which is ported from is_foo. This PR also renames some misported theorems.

@@ -484,7 +484,7 @@ theorem snorm_sub_le_of_dist_bdd {p : ℝ≥0∞} (hp' : p ≠ ∞) {s : Set α}
 #align measure_theory.snorm_sub_le_of_dist_bdd MeasureTheory.snorm_sub_le_of_dist_bdd
 
 /-- A sequence of uniformly integrable functions which converges μ-a.e. converges in Lp. -/
-theorem tendsto_Lp_of_tendsto_ae_of_meas [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
+theorem tendsto_Lp_of_tendsto_ae_of_meas [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
     {f : ℕ → α → β} {g : α → β} (hf : ∀ n, StronglyMeasurable (f n)) (hg : StronglyMeasurable g)
     (hg' : Memℒp g p μ) (hui : UnifIntegrable f p μ)
     (hfg : ∀ᵐ x ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))) :
@@ -555,7 +555,7 @@ set_option linter.uppercaseLean3 false in
 #align measure_theory.tendsto_Lp_of_tendsto_ae_of_meas MeasureTheory.tendsto_Lp_of_tendsto_ae_of_meas
 
 /-- A sequence of uniformly integrable functions which converges μ-a.e. converges in Lp. -/
-theorem tendsto_Lp_of_tendsto_ae [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ℕ → α → β}
+theorem tendsto_Lp_of_tendsto_ae [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞) {f : ℕ → α → β}
     {g : α → β} (hf : ∀ n, AEStronglyMeasurable (f n) μ) (hg : Memℒp g p μ)
     (hui : UnifIntegrable f p μ) (hfg : ∀ᵐ x ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))) :
     Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0) := by
@@ -608,7 +608,7 @@ set_option linter.uppercaseLean3 false in
 /-- Forward direction of Vitali's convergence theorem: if `f` is a sequence of uniformly integrable
 functions that converge in measure to some function `g` in a finite measure space, then `f`
 converge in Lp to `g`. -/
-theorem tendsto_Lp_of_tendstoInMeasure [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
+theorem tendsto_Lp_of_tendstoInMeasure [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
     (hf : ∀ n, AEStronglyMeasurable (f n) μ) (hg : Memℒp g p μ) (hui : UnifIntegrable f p μ)
     (hfg : TendstoInMeasure μ f atTop g) : Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0) := by
   refine' tendsto_of_subseq_tendsto fun ns hns => _
@@ -623,7 +623,7 @@ set_option linter.uppercaseLean3 false in
 
 /-- **Vitali's convergence theorem**: A sequence of functions `f` converges to `g` in Lp if and
 only if it is uniformly integrable and converges to `g` in measure. -/
-theorem tendstoInMeasure_iff_tendsto_Lp [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
+theorem tendstoInMeasure_iff_tendsto_Lp [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
     (hf : ∀ n, Memℒp (f n) p μ) (hg : Memℒp g p μ) :
     TendstoInMeasure μ f atTop g ∧ UnifIntegrable f p μ ↔
       Tendsto (fun n => snorm (f n - g) p μ) atTop (𝓝 0) :=
@@ -794,7 +794,7 @@ theorem uniformIntegrable_const {g : α → β} (hp : 1 ≤ p) (hp_ne_top : p 
 
 /-- This lemma is superceded by `uniformIntegrable_of` which only requires
 `AEStronglyMeasurable`. -/
-theorem uniformIntegrable_of' [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
+theorem uniformIntegrable_of' [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
     (hf : ∀ i, StronglyMeasurable (f i))
     (h : ∀ ε : ℝ, 0 < ε → ∃ C : ℝ≥0,
       ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε) :
@@ -836,7 +836,7 @@ theorem uniformIntegrable_of' [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞
 
 /-- A sequene of functions `(fₙ)` is uniformly integrable in the probability sense if for all
 `ε > 0`, there exists some `C` such that `∫ x in {|fₙ| ≥ C}, fₙ x ∂μ ≤ ε` for all `n`. -/
-theorem uniformIntegrable_of [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
+theorem uniformIntegrable_of [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞)
     (hf : ∀ i, AEStronglyMeasurable (f i) μ)
     (h : ∀ ε : ℝ, 0 < ε → ∃ C : ℝ≥0,
       ∀ i, snorm ({ x | C ≤ ‖f i x‖₊ }.indicator (f i)) p μ ≤ ENNReal.ofReal ε) :
@@ -910,7 +910,7 @@ theorem UniformIntegrable.spec (hp : p ≠ 0) (hp' : p ≠ ∞) (hfu : UniformIn
 
 /-- The definition of uniform integrable in mathlib is equivalent to the definition commonly
 found in literature. -/
-theorem uniformIntegrable_iff [FiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞) :
+theorem uniformIntegrable_iff [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp' : p ≠ ∞) :
     UniformIntegrable f p μ ↔
       (∀ i, AEStronglyMeasurable (f i) μ) ∧
         ∀ ε : ℝ, 0 < ε → ∃ C : ℝ≥0,